Simplifying Square Roots and Rationalizing Denominators

This video tutorial covers Learning Target 10B, focusing on simplifying square roots. It explains the multiplication and division properties of square roots, including how to handle products and quotients of square roots. The tutorial also addresses simplifying square roots with variables and rationalizing the denominator when square roots are present. Through examples, the video demonstrates how to apply these concepts effectively.

What is the multiplication property of square roots?

• The square root of a difference is equal to the difference of the square roots.

• The square root of a sum is equal to the sum of the square roots.

• The square root of a product is equal to the product of the square roots.

• The square root of a quotient is equal to the quotient of the square roots.

How do you simplify the square root of 72?

• By factoring it as 18 times 4 and taking the square root of each factor.

• By factoring it as 9 times 8 and taking the square root of each factor.

• By factoring it as 12 times 6 and taking the square root of each factor.

• By factoring it as 36 times 2 and taking the square root of each factor.

When simplifying the square root of a variable expression, what should you do if the power is divisible by the index?

• Divide the power by the index.

• Multiply the power by the index.

• Subtract the index from the power.

• Add the index to the power.

How do you handle a variable expression where the power is not divisible by the index?

• Break the power into a sum of two terms, one of which is divisible by the index.

• Multiply the power by the index.

• Subtract the index from the power.

• Add the index to the power.

What is the simplified form of the square root of 54x^7?

• 3x^3√6

• 3x^4√6

• 3x^3√6x

• 3x^4√6x

What is the simplified form of 3√2 * 3√2?

• 6√4

• 9√12

• 9√2

• 18√3

When simplifying √2a * √9a³, what is the first step?

• Combine the terms under one square root

• Simplify the square root of 9

• Multiply the coefficients

• Factor out the variables

In the expression 2√7x * 3√14x², what is the simplified form of the variable part?

• x⁴

• x

• x²

• x³

What is the simplified form of √64/49?

• 49/64

• 64/49

• 8/7

• 7/8

To rationalize the denominator of √3/√7, what should you multiply by?

• √3/√3

• √7/√7

• 7/7

• 3/3