What Is The Nearest Whole Number To Each Square Root?a) 155 \sqrt{155} 155 ​ B) 48 \sqrt{48} 48 ​ C) 83 \sqrt{83} 83 ​

Introduction

In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, because 4 multiplied by 4 equals 16. However, not all numbers have a whole number square root. In this article, we will explore the concept of square roots and find the nearest whole number to each of the given square roots: $\sqrt{155}$, $\sqrt{48}$, and $\sqrt{83}$.

What is a Square Root?

A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, because 4 multiplied by 4 equals 16. The square root of a number can be a whole number, a decimal number, or an irrational number. For example, the square root of 9 is 3, which is a whole number. The square root of 2 is an irrational number, which cannot be expressed as a finite decimal or fraction.

Finding the Nearest Whole Number to Each Square Root

To find the nearest whole number to each square root, we need to calculate the square root of each number and then round it to the nearest whole number. We will use the following formulas to calculate the square root:

• $\sqrt{x} = x^{\frac{1}{2}}$
• $\sqrt{x} = \frac{x}{\sqrt{x}}$

We will apply these formulas to each of the given square roots: $\sqrt{155}$, $\sqrt{48}$, and $\sqrt{83}$.

a) $\sqrt{155}$

To find the nearest whole number to $\sqrt{155}$, we need to calculate the square root of 155.

$\sqrt{155} = 155^{\frac{1}{2}}$

Using a calculator, we get:

$\sqrt{155} \approx 12.41$

Rounding 12.41 to the nearest whole number, we get:

$\sqrt{155} \approx 12$

Therefore, the nearest whole number to $\sqrt{155}$ is 12.

b) $\sqrt{48}$

To find the nearest whole number to $\sqrt{48}$, we need to calculate the square root of 48.

$\sqrt{48} = 48^{\frac{1}{2}}$

Using a calculator, we get:

$\sqrt{48} \approx 6.93$

Rounding 6.93 to the nearest whole number, we get:

$\sqrt{48} \approx 7$

Therefore, the nearest whole number to $\sqrt{48}$ is 7.

c) $\sqrt{83}$

To find the nearest whole number to $\sqrt{83}$, we need to calculate the square root of 83.

$\sqrt{83} = 83^{\frac{1}{2}}$

Using a calculator, we get:

$\sqrt{83} \approx 9.13$

Rounding 9.13 to the nearest whole number, we get:

$\sqrt{83} \approx 9$

Therefore, the nearest whole number to $\sqrt{83}$ is 9.

Conclusion

In this article, we explored the concept of square roots and found the nearest whole number to each of the given square roots: $\sqrt{155}$, $\sqrt{48}$, and $\sqrt{83}$. We used the formulas $\sqrt{x} = x^{\frac{1}{2}}$ and $\sqrt{x} = \frac{x}{\sqrt{x}}$ to calculate the square root of each number and then rounded it to the nearest whole number. We found that the nearest whole number to $\sqrt{155}$ is 12, the nearest whole number to $\sqrt{48}$ is 7, and the nearest whole number to $\sqrt{83}$ is 9.

Frequently Asked Questions

• What is a square root?
• How do I find the nearest whole number to a square root?
• What is the formula for calculating the square root of a number?
• How do I use a calculator to find the square root of a number?

References

• [1] Khan Academy. (n.d.). Square Roots. Retrieved from https://www.khanacademy.org/math/algebra/x2f1f6/x2f1f7/x2f1f8
• [2] Math Open Reference. (n.d.). Square Root. Retrieved from https://www.mathopenref.com/sqrt.html
• [3] Wolfram MathWorld. (n.d.). Square Root. Retrieved from https://mathworld.wolfram.com/SquareRoot.html

Further Reading

• [1] Algebra I: Square Roots. (n.d.). Retrieved from https://www.mathway.com/subjects/Algebra-I/Square-Roots
• [2] Square Roots: A Guide to Understanding and Calculating Square Roots. (n.d.). Retrieved from https://www.mathsisfun.com/square-root.html
• [3] Square Roots: A Comprehensive Guide. (n.d.). Retrieved from https://www.mathopenref.com/sqrtguide.html
  

Introduction

In our previous article, we explored the concept of square roots and found the nearest whole number to each of the given square roots: $\sqrt{155}$, $\sqrt{48}$, and $\sqrt{83}$. In this article, we will answer some of the most frequently asked questions about square roots.

Q&A

Q: What is a square root?

A: A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, because 4 multiplied by 4 equals 16.

Q: How do I find the nearest whole number to a square root?

A: To find the nearest whole number to a square root, you need to calculate the square root of the number and then round it to the nearest whole number. You can use a calculator or a formula to calculate the square root.

Q: What is the formula for calculating the square root of a number?

A: The formula for calculating the square root of a number is:

$\sqrt{x} = x^{\frac{1}{2}}$

or

$\sqrt{x} = \frac{x}{\sqrt{x}}$

Q: How do I use a calculator to find the square root of a number?

A: To use a calculator to find the square root of a number, follow these steps:

1. Enter the number into the calculator.
2. Press the square root button (usually denoted by the symbol √).
3. The calculator will display the square root of the number.

Q: What is the difference between a square root and a square?

A: A square root is a value that, when multiplied by itself, gives the original number. A square is the result of multiplying a number by itself. For example, the square root of 16 is 4, but the square of 4 is 16.

Q: Can a square root be a negative number?

A: Yes, a square root can be a negative number. For example, the square root of -16 is -4, because -4 multiplied by -4 equals -16.

Q: Can a square root be an irrational number?

A: Yes, a square root can be an irrational number. For example, the square root of 2 is an irrational number, which cannot be expressed as a finite decimal or fraction.

Q: How do I simplify a square root expression?

A: To simplify a square root expression, you need to find the largest perfect square that divides the number inside the square root. For example, the square root of 18 can be simplified as:

$\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}$

Q: What is the relationship between square roots and exponents?

A: Square roots and exponents are related in that they are inverse operations. For example, the square root of x^2 is x, and the exponent of x^2 is 2.

Conclusion

In this article, we answered some of the most frequently asked questions about square roots. We covered topics such as the definition of a square root, how to find the nearest whole number to a square root, and the relationship between square roots and exponents. We hope that this article has been helpful in clarifying any confusion about square roots.

Frequently Asked Questions

• What is a square root?
• How do I find the nearest whole number to a square root?
• What is the formula for calculating the square root of a number?
• How do I use a calculator to find the square root of a number?
• What is the difference between a square root and a square?
• Can a square root be a negative number?
• Can a square root be an irrational number?
• How do I simplify a square root expression?
• What is the relationship between square roots and exponents?

References

• [1] Khan Academy. (n.d.). Square Roots. Retrieved from https://www.khanacademy.org/math/algebra/x2f1f6/x2f1f7/x2f1f8
• [2] Math Open Reference. (n.d.). Square Root. Retrieved from https://www.mathopenref.com/sqrt.html
• [3] Wolfram MathWorld. (n.d.). Square Root. Retrieved from https://mathworld.wolfram.com/SquareRoot.html

Further Reading

• [1] Algebra I: Square Roots. (n.d.). Retrieved from https://www.mathway.com/subjects/Algebra-I/Square-Roots
• [2] Square Roots: A Guide to Understanding and Calculating Square Roots. (n.d.). Retrieved from https://www.mathsisfun.com/square-root.html
• [3] Square Roots: A Comprehensive Guide. (n.d.). Retrieved from https://www.mathopenref.com/sqrtguide.html