# How you simplify (Square root of 75) +(square root of 48)?

Jul 27, 2015

= color(blue)(9sqrt3

#### Explanation:

• 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 $2$ and $3$ as its prime factors)

So,
$\sqrt{75} = \sqrt{5 \cdot 5 \cdot 3} = \sqrt{{5}^{2} \cdot 3} = 5 \sqrt{3}$

$\sqrt{48} = \sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 3} = \sqrt{{2}^{2} \cdot {2}^{2} \cdot 3} = 4 \sqrt{3}$

Now,
sqrt75 +sqrt48 = 5sqrt3+4sqrt3 = color(blue)(9sqrt3