Question

simplify √45 - 3√20 + 4√5 ( step wise)

Answer 1

Hi
To simplify the given problem
We have to convert each surd into
K(root a) form
Where. 'a' is the Least positive rational number and K is a rational number.

i) sqrt(45) = sqrt [(3×3)×5] = 3 sqrt 5

ii)3 sqrt(20) = 3 sqrt [ (2 × 2) ×5 ] = 3×2 sqrt 5 =6 sqrt 5

iii)4 sqrt 5
Now simplify the given problem

Sqrt 45 - 3 sqrt 20 + 4 sqrt 5

=3 sqrt 5 - 6 sqrt 5 + 4 sqrt 5

= (3 - 6 + 4) sqrt 5

=(7 - 6 ) sqrt 5
= sqrt 5
Hope this will helps you

Answer 2

Step-by-step explanation:

$\bf \underline{Solution-}$

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

$\sf{ = \sqrt{9 \times 5} - 3 \sqrt{4 \times 5} + 4 \sqrt{5} }$

$\sf{ = 3 \sqrt{5} - 3 \times 2 \sqrt{5} + 4 \sqrt{5} }$

$\sf{ = (3 - 6 + 4) \sqrt{5} }$

$\sf{ = \sqrt{5} } \: \: \: \: \bf{Ans.}$