Simplify. Rationalize the denominator. 8/-5 - sqrt 2 ______

Find Conjugate: Select the conjugate of -5 - sqrt(2). Conjugate of a - sqrt(b): a + sqrt(b) Conjugate of -5 - sqrt(2): -5 + sqrt(2)Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. To rationalize the denominator, we multiply the expression by the conjugate of the denominator over itself, which is 1. (8 * (-5 + sqrt(2))) / ((-5 - sqrt(2)) * (-5 + sqrt(2)))Simplify Numerator: Simplify the numerator. 8 * (-5 + sqrt(2)) = 8 * -5 + 8 * sqrt(2) = -40 + 8 * sqrt(2)Simplify Denominator: Simplify the denominator using the difference of squares formula. (-5 - sqrt(2)) * (-5 + sqrt(2)) = (-5)^2 - (sqrt(2))^2 = 25 - 2 = 23Write Simplified Expression: Write the simplified expression. The simplified expression is (-40 + 8 * sqrt(2)) / 23

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. Rationalize the denominator. $\newline$ $\frac{8}{-5 - \sqrt{2}}$

View step-by-step help

Home

Math Problems

Algebra 1

Simplify radical expressions using conjugates

Full solution

Q. Simplify. Rationalize the denominator.

\newline

\frac{8}{-5 - \sqrt{2}}

Find Conjugate: Select the conjugate of $-5 - \sqrt{2}$ . $\newline$ Conjugate of $a - \sqrt{b}$ : $a + \sqrt{b}$ $\newline$ Conjugate of $-5 - \sqrt{2}$ : $-5 + \sqrt{2}$
Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. $\newline$ To rationalize the denominator, we multiply the expression by the conjugate of the denominator over itself, which is $1$ . $\newline$ $\frac{8 \cdot (-5 + \sqrt{2})}{(-5 - \sqrt{2}) \cdot (-5 + \sqrt{2})}$
Simplify Numerator: Simplify the numerator. $\newline$ $8 \times (-5 + \sqrt{2}) = 8 \times -5 + 8 \times \sqrt{2} = -40 + 8 \times \sqrt{2}$
Simplify Denominator: Simplify the denominator using the difference of squares formula. $\newline$ $(-5 - \sqrt{2}) * (-5 + \sqrt{2}) = (-5)^2 - (\sqrt{2})^2 = 25 - 2 = 23$
Write Simplified Expression: Write the simplified expression. $\newline$ The simplified expression is $(-40 + 8 \times \sqrt{2}) / 23$