Rationalize 5√7−7√5√7−√5

Question 1 Report

Rationalize $\frac{5 \sqrt{7} - 7 \sqrt{5}}{\sqrt{7} - \sqrt{5}}$

-2 \sqrt{35}\)

4\sqrt{7}\) - 6

\sqrt{5}

-√35

4\sqrt{7}\) - 8

\sqrt{5}

√35

Answer Details

$\frac{5 \sqrt{7} - 7 \sqrt{5}}{\sqrt{7} - \sqrt{5}}$ = $\frac{5 \sqrt{7} - 7 \sqrt{5}}{\sqrt{7} - \sqrt{5}}$ x $\frac{\sqrt{7} + \sqrt{5}}{\sqrt{7} + \sqrt{5}}$
= $\frac{(5 \times 7) + (5 \sqrt{7} \times 5) - (7 \times \sqrt{5} \times 7) (- 7 \times 5)}{(\sqrt{7})^{2}}$
= $\frac{5 \sqrt{35} - 7 \sqrt{35}}{2}$
= $\frac{- 2 \sqrt{35}}{2}$
= - $\sqrt{35}$

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Positive And Negative Integers, Rational Numbers

Surds (radicals)

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