Question

Simplify 5√300+ 2√75 - 4√108​

Answer 1

Answer:

Square root of a number can be simplified by prime factorising the number.

Prime factorisation involves expressing a number as a product of prime numbers.

(75 has 3 and 5 as its prime factors and 48 has 2and 3 as its prime factors)

So,

√75=√5⋅5⋅3=√52⋅3=5√3

√48=√2⋅2⋅2⋅2⋅3=√22⋅22⋅3=4√3

Now,

√75+√48=5√3+4√3=9√3

Explanation:

Answer 2

Answer:

36√3

Explanation:

$5\sqrt{300} + 2 \sqrt{75} - 4 \sqrt{108} \\ = 5 \sqrt{100 \times 3} + 2 \sqrt{25 \times 3} - 4 \sqrt{36\times 3} \\ = (5 \times 10 \sqrt{3} ) + (2 \times 5 \sqrt{3} ) - (4 \times 6 \sqrt{3} ) \\ = 50 \sqrt{3} + 10 \sqrt{3} - 24 \sqrt{3} \\ = 60 \sqrt{3} - 24 \sqrt{3} \\ = 36 \sqrt{3}$

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