Which Choices Are Equivalent To The Expression Below? Check All That Apply.$\sqrt{8} \cdot \sqrt{8}$A. $\sqrt{64}$ B. 64 C. $\sqrt{16}$ D. 8 E. $\sqrt{6} \cdot 8$ F. $\sqrt{8}$

Which Choices are Equivalent to the Expression Below?

Understanding the Given Expression

The given expression is $\sqrt{8} \cdot \sqrt{8}$. To simplify this expression, we need to understand the properties of square roots. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, we have the square root of 8 multiplied by itself.

Simplifying the Expression

To simplify the expression, we can start by multiplying the two square roots together. This gives us:

$\sqrt{8} \cdot \sqrt{8} = \sqrt{8 \cdot 8}$

Using the property of square roots that $\sqrt{a} \cdot \sqrt{a} = \sqrt{a^2}$, we can simplify the expression further:

$\sqrt{8 \cdot 8} = \sqrt{64}$

Evaluating the Choices

Now that we have simplified the expression, we can evaluate the choices given:

A. $\sqrt{64}$: This is equivalent to the simplified expression we obtained.

B. 64: This is not equivalent to the simplified expression, as it is the result of squaring the square root of 64, not the square root of 8 multiplied by itself.

C. $\sqrt{16}$: This is not equivalent to the simplified expression, as it is the square root of 16, not 64.

D. 8: This is not equivalent to the simplified expression, as it is the square root of 8, not 64.

E. $\sqrt{6} \cdot 8$: This is not equivalent to the simplified expression, as it involves multiplying the square root of 6 by 8, not the square root of 8 by itself.

F. $\sqrt{8}$: This is not equivalent to the simplified expression, as it is the square root of 8, not 64.

Conclusion

Based on our simplification of the expression and evaluation of the choices, we can conclude that the correct answer is:

• A. $\sqrt{64}$

This is the only choice that is equivalent to the simplified expression $\sqrt{64}$. The other choices do not match the simplified expression and are therefore incorrect.
Which Choices are Equivalent to the Expression Below? - Q&A

Q: What is the property of square roots that allows us to simplify the expression $\sqrt{8} \cdot \sqrt{8}$?

A: The property of square roots that allows us to simplify the expression $\sqrt{8} \cdot \sqrt{8}$ is $\sqrt{a} \cdot \sqrt{a} = \sqrt{a^2}$. This property states that when we multiply two square roots together, we can combine them into a single square root of the product of the two numbers.

Q: How do we simplify the expression $\sqrt{8} \cdot \sqrt{8}$ using this property?

A: To simplify the expression $\sqrt{8} \cdot \sqrt{8}$, we can multiply the two square roots together and then apply the property $\sqrt{a} \cdot \sqrt{a} = \sqrt{a^2}$. This gives us:

$\sqrt{8} \cdot \sqrt{8} = \sqrt{8 \cdot 8} = \sqrt{64}$

Q: Why is choice B, 64, not equivalent to the simplified expression?

A: Choice B, 64, is not equivalent to the simplified expression because it is the result of squaring the square root of 64, not the square root of 8 multiplied by itself. In other words, 64 is the result of $\sqrt{64} \cdot \sqrt{64}$, not $\sqrt{8} \cdot \sqrt{8}$.

Q: Why is choice C, $\sqrt{16}$, not equivalent to the simplified expression?

A: Choice C, $\sqrt{16}$, is not equivalent to the simplified expression because it is the square root of 16, not 64. The simplified expression is $\sqrt{64}$, not $\sqrt{16}$.

Q: Why is choice D, 8, not equivalent to the simplified expression?

A: Choice D, 8, is not equivalent to the simplified expression because it is the square root of 8, not 64. The simplified expression is $\sqrt{64}$, not $\sqrt{8}$.

Q: Why is choice E, $\sqrt{6} \cdot 8$, not equivalent to the simplified expression?

A: Choice E, $\sqrt{6} \cdot 8$, is not equivalent to the simplified expression because it involves multiplying the square root of 6 by 8, not the square root of 8 by itself. The simplified expression is $\sqrt{64}$, not $\sqrt{6} \cdot 8$.

Q: Why is choice F, $\sqrt{8}$, not equivalent to the simplified expression?

A: Choice F, $\sqrt{8}$, is not equivalent to the simplified expression because it is the square root of 8, not 64. The simplified expression is $\sqrt{64}$, not $\sqrt{8}$.

Conclusion

In this Q&A article, we have discussed the property of square roots that allows us to simplify the expression $\sqrt{8} \cdot \sqrt{8}$ and evaluated the choices given. We have concluded that the correct answer is:

• A. $\sqrt{64}$

This is the only choice that is equivalent to the simplified expression $\sqrt{64}$. The other choices do not match the simplified expression and are therefore incorrect.