Simplifying Square Roots with Variables

The video tutorial explains how to simplify square roots by identifying perfect square factors. It covers two examples: simplifying the square root of 49x^18 and negative three times the square root of 121x^34. The tutorial emphasizes the importance of recognizing perfect squares and explains the process of simplifying expressions with even and odd exponents, assuming all variables are positive.

What is the first step in simplifying the square root of 49x^18?

• Subtract 18 from 49.

• Multiply 49 by x^18.

• Divide 49 by 2.

• Identify if 49 and x^18 are perfect squares.

Why is 49 considered a perfect square?

• Because it is a prime number.

• Because it is less than 50.

• Because it is an odd number.

• Because it is equal to 7 times 7.

How can x^18 be expressed to show it is a perfect square?

• x^18 = x^2 * x^16

• x^18 = x^12 * x^6

• x^18 = x^6 * x^3

• x^18 = x^9 * x^9

What does the square root of 49 simplify to?

• 14

• 7

• 7^2

• 49

What is the simplified form of the square root of x^18?

• x^18

• x^3

• x^9

• x^6

What is the next example discussed after simplifying the square root of 49x^18?

• -3 times the square root of 121x^34

• The square root of 100x^25

• The cube root of 27x^15

• The square root of 64x^20

Why is 121 considered a perfect square?

• Because it is greater than 100.

• Because it is a prime number.

• Because it is an even number.

• Because it is equal to 11 times 11.

How can x^34 be expressed to show it is a perfect square?

• x^34 = x^16 * x^18

• x^34 = x^17 * x^17

• x^34 = x^12 * x^22

• x^34 = x^2 * x^32

What does the square root of 121 simplify to?

• 11

• 22

• 121

• 11^2

What is the simplified form of -3 times the square root of 121x^34?

• -33x^17

• -33x^34

• -3x^17

• -3x^34