Question

Rationalize the denominator
√2+√45/√2+√7-2√10

Answer 1

Answer:

√2 (2 - √5 + √14) / 2

Step-by-step explanation:

Rationalizing the denominator means making the denominator of the expression a rational number.

A rational number is actually a part of a whole which can be expressed as a decimal, fraction or a percentage.

√2+√45/√2+√7-2√10

Taking √2 as L.C.M;

= (√2 √2 + √45 + √7 √2 - 2√10 √2) / √2

= (2 + √9 √5 + √14 - 2 √20) / √2

= (2 + 3 √5 + √14 - 2 √4 √5) / √2

= (2 + 3 √5 + √14 - 4 √5) / √2

= (2 - √5 + √14) / √2

Multiplying the numerator and the denominator with √2

= √2 (2 - √5 + √14) / 2