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Maths-

General

Easy

Question

Simplify √45 - 3√20 +4√5

hint Hint:

Use prime factorization.

The correct answer is: √5

Complete step by step solution:
On prime factorization, we can write
$square root of 45 equals square root of 3 cross times 3 cross times 5 end root comma 3 square root of 20 equals 3 cross times square root of 2 cross times 2 cross times 5 end root text and end text 4 square root of 5 equals 4 square root of 5$
This can be written as $3 square root of 5 comma 6 square root of 5$ and $4 square root of 5$ respectively.
So, $square root of 45 minus 3 square root of 20 plus 4 square root of 5 equals 3 square root of 5 minus 6 square root of 5 plus 4 square root of 5 equals 1 square root of 5 equals square root of 5$

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