Question

6. Simplify each of the following by rationalising the denominator:
root 7- root 5 root 7+root5​

Answer 1

Answer:

Step-by-step explanation:

6-\sqrt{35}

Here, the given expression is,

\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}

For rationalizing the denominator,

Multiply both numerator and denominator by √7 - √5,

\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}\times \frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}-\sqrt{5}}

=\frac{(\sqrt{7}-\sqrt{5})^2}{(\sqrt{7})^2-(\sqrt{5})^2}

=\frac{7+5-2\times \sqrt{7}\times \sqrt{5}}{7-5}

=\frac{12-2\sqrt{35}}{2}

=6-\sqrt{35}

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Answer 2

Answer:

Step-by-step explanation:

Combine using the products for radicals

√7

−

√ 7

⋅

5

+

√ 5

 

Multiply  

7

by  

5

.

√7

−

√ 35

+

√5

The result can be shown in multiple forms.

Exact Form:

√7

−

√ 35

+

√ 5

Decimal Form:

−

1.03426049

…