Operations with Square Roots

How do you subtract square roots?

• You can subtract square roots only if they are like terms, for example, @@3\sqrt{2} - 2\sqrt{2} = 1\sqrt{2}@@.

• You can subtract square roots by simply subtracting the numbers under the square root.

• You can subtract square roots by multiplying them together.

• You can subtract square roots by adding their coefficients.

• Take the square root of the number directly without any further simplification.

• Add 1 to the number under the root before taking the square root.

• Multiply the number under the root by 2 before simplifying.

How do you rationalize the denominator?

• Multiply the numerator and denominator by the square root of the denominator.

• Add the numerator and denominator together.

• Divide the numerator by the denominator.

• Subtract the denominator from the numerator.

What is the square root of a perfect square?

• An integer

• A fraction

• A decimal

• A negative number

What is the sum of square roots?

• The sum of square roots can be simplified like products.

• The sum of square roots cannot be simplified in the same way as products.

• The sum of square roots is always an integer.

• The sum of square roots is equal to the product of the numbers.

What is the square root of a negative number?

• It is a real number.

• It is expressed in terms of imaginary numbers.

• It is always zero.

• It is undefined.

What is the difference between rational and irrational square roots?

• Rational square roots are the square roots of perfect squares (e.g., @@\sqrt{4} = 2@@), while irrational square roots are not perfect squares (e.g., @@\sqrt{2}@@ is irrational).

• Rational square roots are always integers, while irrational square roots are always fractions.

• Rational square roots can be negative, while irrational square roots are always positive.

• Rational square roots are the square roots of any number, while irrational square roots are only those that cannot be simplified.

What is the value of @@\sqrt{64}@@?

• 6

• 7

• 8

• 9

How do you combine like terms with square roots?

• Combine like terms by multiplying the coefficients of the square roots.

• Combine like terms by adding or subtracting the coefficients of the square roots. For example, @@3\sqrt{2} + 2\sqrt{2} = 5\sqrt{2}@@.

• Combine like terms by ignoring the coefficients and only adding the square roots.

• Combine like terms by taking the average of the coefficients of the square roots.

What is the product of two square roots?

• If a, b are non-negative, then @@\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}@@

• If a, b are non-negative, then @@\sqrt{a} + \sqrt{b} = \sqrt{a + b}@@

• If a, b are non-negative, then @@\sqrt{a} - \sqrt{b} = \sqrt{a - b}@@

• If a, b are non-negative, then @@\sqrt{a} \div \sqrt{b} = \sqrt{\frac{a}{b}}@@