Question

Simplify: √45 – 3 √20 + 4 √5​

Answer 1

Answer:

First step : √45 - 3√20 + 4√5

Second: 3√5 -3*2√5 +4√5

Third: 3√5-6√5+4√5

Fourth: (3-6+4)√5

Fifth: (-3+4)√5

Answer= √5

(We had to separate the root 5 from all other terms. (Since it was common) Then on the basis of prime factorization we took out the factors of 45 and 20, where we multiplied the other numbers and separated the root 5)

That way, 45 became root 3*3*5 and 20 became 2*2*5.

This is where we get the common root 5

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

$\bf \underline{Solution-}$

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

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

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

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

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