Which Of The Following Are Like Radicals? Check All Of The Boxes That Apply.- 3 X X 2 Y 3x \sqrt{x^2 Y} 3 X X 2 Y ​ - − 12 X X 2 Y -12x \sqrt{x^2 Y} − 12 X X 2 Y ​ - − 2 X X Y 2 -2x \sqrt{xy^2} − 2 X X Y 2 ​ - X Y X 2 X \sqrt{yx^2} X Y X 2 ​ - − X X 2 Y 2 -x \sqrt{x^2 Y^2} − X X 2 Y 2 ​ - 2 X 2 Y 2 \sqrt{x^2 Y} 2 X 2 Y ​

What are Like Radicals?

Like radicals are mathematical expressions that contain the same type of radical, which is typically denoted by the symbol √. In other words, like radicals are expressions that have the same index (or root) and the same radicand (the expression inside the radical). When we have like radicals, we can combine them by adding or subtracting their coefficients.

Checking for Like Radicals

To determine if two or more radicals are like radicals, we need to compare their indices and radicands. If they have the same index and radicand, then they are like radicals.

Analyzing the Given Expressions

Let's analyze the given expressions and check which ones are like radicals.

Expression 1: $3x \sqrt{x^2 y}$

This expression contains a radical with an index of 2 and a radicand of $x^2 y$. We can rewrite this expression as $3x \sqrt{(xy)^2}$.

Expression 2: $-12x \sqrt{x^2 y}$

This expression also contains a radical with an index of 2 and a radicand of $x^2 y$. We can rewrite this expression as $-12x \sqrt{(xy)^2}$.

Expression 3: $-2x \sqrt{xy^2}$

This expression contains a radical with an index of 2 and a radicand of $xy^2$. We can rewrite this expression as $-2x \sqrt{(xy)^2}$.

Expression 4: $x \sqrt{yx^2}$

This expression contains a radical with an index of 2 and a radicand of $yx^2$. We can rewrite this expression as $x \sqrt{(xy)^2}$.

Expression 5: $-x \sqrt{x^2 y^2}$

This expression contains a radical with an index of 2 and a radicand of $x^2 y^2$. We can rewrite this expression as $-x \sqrt{(xy)^2}$.

Expression 6: $2 \sqrt{x^2 y}$

This expression contains a radical with an index of 2 and a radicand of $x^2 y$. We can rewrite this expression as $2 \sqrt{(xy)^2}$.

Comparing the Expressions

Now that we have rewritten the expressions, let's compare them to determine which ones are like radicals.

• Expressions 1 and 2 have the same index and radicand, so they are like radicals.
• Expressions 3 and 4 have the same index and radicand, so they are like radicals.
• Expressions 5 and 6 have the same index and radicand, so they are like radicals.
• Expressions 1 and 3 have different radicands, so they are not like radicals.
• Expressions 2 and 4 have different radicands, so they are not like radicals.
• Expressions 1 and 5 have different radicands, so they are not like radicals.
• Expressions 2 and 6 have different radicands, so they are not like radicals.
• Expressions 3 and 5 have different radicands, so they are not like radicals.
• Expressions 4 and 6 have different radicands, so they are not like radicals.

Conclusion

In conclusion, the like radicals among the given expressions are:

• $3x \sqrt{x^2 y}$ and $-12x \sqrt{x^2 y}$
• $-2x \sqrt{xy^2}$ and $x \sqrt{yx^2}$
• $-x \sqrt{x^2 y^2}$ and $2 \sqrt{x^2 y}$

Q: What are like radicals?

A: Like radicals are mathematical expressions that contain the same type of radical, which is typically denoted by the symbol √. In other words, like radicals are expressions that have the same index (or root) and the same radicand (the expression inside the radical).

Q: How do I determine if two or more radicals are like radicals?

A: To determine if two or more radicals are like radicals, you need to compare their indices and radicands. If they have the same index and radicand, then they are like radicals.

Q: What is the difference between like radicals and unlike radicals?

A: Unlike radicals are mathematical expressions that contain different types of radicals. Unlike radicals cannot be combined by adding or subtracting their coefficients.

Q: Can I add or subtract the coefficients of unlike radicals?

A: No, you cannot add or subtract the coefficients of unlike radicals. Unlike radicals must be simplified separately before they can be combined.

Q: Can I simplify unlike radicals?

A: Yes, you can simplify unlike radicals by rewriting them in a form that has the same index and radicand.

Q: How do I simplify unlike radicals?

A: To simplify unlike radicals, you need to rewrite them in a form that has the same index and radicand. This can be done by factoring the radicand and rewriting it in a form that has the same index and radicand.

Q: What is the rule for adding and subtracting like radicals?

A: The rule for adding and subtracting like radicals is to add or subtract their coefficients while keeping the same index and radicand.

Q: Can I add or subtract the coefficients of like radicals with different indices?

A: No, you cannot add or subtract the coefficients of like radicals with different indices. Like radicals with different indices must be simplified separately before they can be combined.

Q: Can I add or subtract the coefficients of like radicals with different radicands?

A: No, you cannot add or subtract the coefficients of like radicals with different radicands. Like radicals with different radicands must be simplified separately before they can be combined.

Q: What is the difference between like radicals and similar radicals?

A: Similar radicals are mathematical expressions that contain the same type of radical, but have different coefficients. Like radicals are mathematical expressions that contain the same type of radical and have the same index and radicand.

Q: Can I add or subtract the coefficients of similar radicals?

A: Yes, you can add or subtract the coefficients of similar radicals.

Q: Can I add or subtract the coefficients of like radicals?

A: Yes, you can add or subtract the coefficients of like radicals.

Q: What is the rule for multiplying like radicals?

A: The rule for multiplying like radicals is to multiply their coefficients and keep the same index and radicand.

Q: Can I multiply like radicals with different indices?

A: No, you cannot multiply like radicals with different indices. Like radicals with different indices must be simplified separately before they can be combined.

Q: Can I multiply like radicals with different radicands?

A: No, you cannot multiply like radicals with different radicands. Like radicals with different radicands must be simplified separately before they can be combined.

Q: What is the rule for dividing like radicals?

A: The rule for dividing like radicals is to divide their coefficients and keep the same index and radicand.

Q: Can I divide like radicals with different indices?

A: No, you cannot divide like radicals with different indices. Like radicals with different indices must be simplified separately before they can be combined.

Q: Can I divide like radicals with different radicands?

A: No, you cannot divide like radicals with different radicands. Like radicals with different radicands must be simplified separately before they can be combined.

Conclusion

In conclusion, like radicals are mathematical expressions that contain the same type of radical, which is typically denoted by the symbol √. To determine if two or more radicals are like radicals, you need to compare their indices and radicands. If they have the same index and radicand, then they are like radicals.