Question

Solve Q1



both the Parts
A part

and

B part

Answer 1

1.Simplyfy

a. √45 - 3√20+4√5
=9√5 - 12√5 + 4√5
=(9-12+4)√5
=(13-12)√5
= √5 Ans.

b.3√3+2√27+7/√3
=3√3+18√3+3/7√3
=(3+18+3/7)√3
=(21+3/7)√3
={(147+3)/7}√3
=(150/7)√3

Answer 2

Heya !!

a)

$\sqrt{45} - 3 \sqrt{20} + 4 \sqrt{5}$

On splitting we get,

$= \sqrt{3 \times 3 \times 5} - 3 \sqrt{2 \times 2 \times 5} + 4 \sqrt{5} \\ \\ = \sqrt{ {3}^{2} \times 5 } - 3 \sqrt{ {2}^{2} \times 5} + 4 \sqrt{5} \\ \\ = 3 \sqrt{5} - 3 \times 2 \sqrt{5} + 4 \sqrt{5} \\ \\ = 3 \sqrt{5} - 6 \sqrt{5} + 4 \sqrt{5} \\ \\ = 3 \sqrt{5} + 4 \sqrt{5} - 6 \sqrt{5} \\ \\ = 7 \sqrt{5} - 6 \sqrt{5} \\ \\ = \sqrt{5}$

b)

$3 \sqrt{3} + 2 \sqrt{27} + \frac{7}{ \sqrt{3} }$

On splitting we get,

$= 3 \sqrt{3} + 2 \sqrt{3 \times 3 \times 3} + \frac{7}{ \sqrt{3} } \\ \\ = 3 \sqrt{3} + 2 \sqrt{ {3}^{2} \times 3} + \frac{7}{\sqrt{3} } \\ \\ = 3 \sqrt{3} + 2 \times 3 \sqrt{3} + \frac{7}{ \sqrt{3} } \\ \\ = 3 \sqrt{3} + 6 \sqrt{3} + \frac{7}{ \sqrt{3} }$

On rationalizing the denominator we get,


$= 3 \sqrt{3} + 6 \sqrt{3} + \frac{7}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } \\ \\ = 9 \sqrt{3} + \frac{7 \sqrt{3} }{ {( \sqrt{3}) }^{2} } \\ \\ = 9 \sqrt{3} + \frac{7 \sqrt{3} }{3} \\ \\ = \frac{9 \sqrt{3} \times 3 + 7 \sqrt{3} }{3} \\ \\ = \frac{27 \sqrt{3} + 7 \sqrt{3} }{3} \\ \\ = \frac{34 \sqrt{3} }{3}$

Hope this helps ☺