# How do you simplify sqrt72-sqrt50?

Nov 6, 2015

$\sqrt{72} - \sqrt{50} = \sqrt{2}$

#### Explanation:

$\sqrt{72} - \sqrt{50}$

Write the prime factors for $72$.

$\sqrt{2 \times 2 \times 2 \times 3 \times 3} - \sqrt{50}$

Group like terms in pairs.

$\sqrt{\left(2 \times 2\right) \times 2 \times \left(3 \times 3\right)} - \sqrt{50}$

Simplify.

$\sqrt{{2}^{2} \times 2 \times {3}^{2}} - \sqrt{50}$

Apply square root rule $\sqrt{{a}^{2}} = a$

$2 \times 3 \sqrt{2} - \sqrt{50}$

$6 \sqrt{2} - \sqrt{50}$

Write the prime factors for $50$.

$6 \sqrt{2} - \sqrt{2 \times 5 \times 5}$

Group like terms in pairs.

$6 \sqrt{2} - \sqrt{2 \times \left(5 \times 5\right)}$

Simplify.

$6 \sqrt{2} - \sqrt{2 \times {5}^{2}}$

Apply square root rule $\sqrt{{a}^{2}} = a$

$6 \sqrt{2} - 5 \sqrt{2} =$

$\sqrt{2}$