Question

5√3+3√5 / 5√3-3√5 ratinalise the denominator with steps​

Answer 1

Answer:

Step-by-step explanation:

5√3+3√5 / 5√3-3√5

= (5√3+3√5)(5√3+3√5) / (5√3-3√5)(5√3+3√5)

= ((5√3)² + (3√5)² + 2 (5√3)(3√5)) / ((5√3)² - (3√5)²)

= (75 + 45 + 30√15) / (75-45)

= (120 + 30√15) / 30

= 30(4+√15) / 30

= 4 + √15

Answer 2

The correct answer is 4+√15.

Given:

The fraction (5√3+3√5)/(5√3-3√5).

To Find:

The rationalized form of the given fraction.

Solution:

By rationalizing a given fraction, we are eliminating the terms having roots in the denominator.

To rationalize a fraction of the form (a+b)/(c+d), we need to multiply both the numerator and the denominator by the conjugate of the denominator, i.e. by (c-d).

We have the fraction (5√3+3√5)/(5√3-3√5).

The conjugate of its denominator = (5√3+3√5)

Multiplying the conjugate of the denominator to both the numerator and the denominator, we have:

$\frac{5\sqrt{3}+3\sqrt{5} }{5\sqrt{3}-3\sqrt{5}}$ x $\frac{5\sqrt{3}+3\sqrt{5} }{5\sqrt{3}+3\sqrt{5}}$ = $\frac{(5\sqrt{3}+3\sqrt{5})^2 }{(5\sqrt{3})^2-(3\sqrt{5})^2}$ = $\frac{(5\sqrt{3})^2+2(5\sqrt{3})(3\sqrt{5})+(3\sqrt{5})^2 }{(5\sqrt{3})^2-(3\sqrt{5})^2}$

= `$\frac{120+30\sqrt{15} }{30}$ =  4+√15.

∴ The correct answer is 4+√15.

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