Find the square of each radical expression. See Example 2.

√2
3

Question

Find the square of each radical expression. See Example 2.

√2
 3

Accepted Answer

Hey, everyone here we are asked to determine the square of the following expression, the square root of 11 divided by seven. Here we have four answer choice options, answer choice A 11 divided by 49 answer B 11 divided by seven, answer C 121 divided by seven, answer D 121 divided by 49. So the first thing we need to recall with this problem here is that when we determine the square of some expression, that means we take the entire expression and raise it to the power of two. So now we just want to distribute the square to the numerator and the denominator of our expression. So we have the square root of 11 raised to the power of two divided by seven squared. So now we just want to begin simplifying. So in the denominator again, we just have seven squared. So this simplifies 249. And now in the numerator, we have this square root of 11. So we first want to recall that when we take the square root of some expression, that is equivalent to raising that expression to the power of one half. So rewriting, we have the quantity of 11 raised to the power of one half and then raised to the power of two. And now we just want to recall the power to a power rule which states that A raised to the power of M and then raised to the power of N is equivalent to a, raised to the power of M multiplied by N. So this power rule, these, this power to a power rule tells us that we can simply multiply our two exponents together. So doing this, we can rewrite our expression as 11 raised to the power of two divided by two. And this is still all divided by 49. Now, just continuing to simplify the exponent, we have 11 raised to the power of one divided by 49. And now to finish simplifying, we just have to recall that when we have an expression raised to the power of one, it is equivalent to just the expression itself. So rewriting our expression, we just have 11 divided by 49. So this is our final simplified answer which leaves us with answer choice. A 11 divided by 49. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Find the square of each radical expression. See Example 2. √2 3

Key Concepts

Radical Expressions

Squaring a Radical

Properties of Exponents

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