Simplify the rational and irrational numbers:

by

Simplify:

[7√3 / (√10 + √3)] – [2√5 / (√6 + √5)] – [3√2 / (√15 + 3√2)]

Solution:

Let us simplify individually,
[7√3 / (√10 + √3)]
Let us rationalize the denominator,
7√3 / (√10 + √3) = [7√3(√10 – √3)] / [(√10 + √3) (√10 – √3)]
= [7√3.√10 – 7√3.√3] / [(√10)2 – (√3)2]
= [7√30 – 7.3] / [10 – 3]
= 7[√30 – 3] / 7
= √30 – 3
Now,
[2√5 / (√6 + √5)]
Let us rationalize the denominator, we get
2√5 / (√6 + √5) = [2√5 (√6 – √5)] / [(√6 + √5) (√6 – √5)]
= [2√5.√6 – 2√5.√5] / [(√6)2 – (√5)2]
= [2√30 – 2.5] / [6 – 5]
= [2√30 – 10] / 1
= 2√30 – 10
Now,
[3√2 / (√15 + 3√2)]
Let us rationalize the denominator, we get
3√2 / (√15 + 3√2) = [3√2 (√15 – 3√2)] / [(√15 + 3√2) (√15 – 3√2)]
= [3√2.√15 – 3√2.3√2] / [(√15)2 – (3√2)2]
= [3√30 – 9.2] / [15 – 9.2]
= [3√30 – 18] / [15 – 18]
= 3[√30 – 6] / [-3]
= [√30 – 6] / -1
= 6 – √30
So, according to the question let us substitute the obtained values,
[7√3 / (√10 + √3)] – [2√5 / (√6 + √5)] – [3√2 / (√15 + 3√2)]
= (√30 – 3) – (2√30 – 10) – (6 – √30)
= √30 – 3 – 2√30 + 10 – 6 + √30
= 2√30 – 2√30 – 3 + 10 – 6
= 1

More Solution:

Leave a Comment