Question

Rationlise 5 by root 7- root 5

Answer 1

Given

Rationalize

5/√7 - √5

Solution

→ 5/√7 - √5

★ Rationalize the denominator

→ 5/√7 - √5 × √7 + √5/√7 + √5

★ Apply identity : a² - b² = (a +b)(a -b)

→ 5(√7 + √5)/(√7)² - (√5)²

→ 5√7 + 5√5/7 - 5

→ 5√7 + 5√5/2

Some identities

• (a +b)² = a² + b² + 2ab
• (a -b)² = a² + b² - 2ab
• a³ + b³ = (a +b)(a² -ab+b²)
• a³ - b³ = (a -b)(a² +ab+b²)

Answer 2

Hey mate !! Here you go :-

As you know,

Rationalize means we have to multiply the given number by such a rationalizing factor such that the irrational number in the denominator is replaced by a rational number.

Rationalizing factor-It is the number by which we need to multiply the given number so that the denominator becomes a rational number.

Here,If their is a binomial in the denominator then the rationalizing factor will be the denominator with opposite sign,SEE BELOW--

By,using (a+b)(a-b)= $a^{2}$-$b^{2}$

$\frac{5}{7- \sqrt{5} }$ * $\frac{7+\sqrt{5} }{7+\sqrt{5} }$= $\frac{35+5\sqrt{5} }}$$\frac{35+5\sqrt{5} }{49-5}$=$\frac{35+5\sqrt{5} }{44}$=Answer

Now the denominator is a rational number

You have rationalized the number !!

HOPE THAT HELPS YOU,

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