Question

Simplify the following surds : √75 – √27 *​

Answer 1

Answer:

$\sqrt{75} -\sqrt{27}$ = $2\sqrt{3}$

Step-by-step explanation:

We know that,

75 = 25×3 = 3×5²

27 = 9×3 = 3×3²

Substituting this value in we get,

$\implies$ $\sqrt{75} -\sqrt{27}$

$\implies$ $\sqrt{3 \times 5^2} -\sqrt{3 \times 3^2}$

$\implies$ $5\sqrt{3} -3\sqrt{3}$

$\implies$ $2\sqrt{3}$

Answer 2

$\:\:\:\:\:\:\:\sqrt{75} - \sqrt{27} \\ \\ = \:\:\sqrt{5 \times 5 \times 3} - \sqrt{3 \times 3 \times 3} \\ \\ = \sqrt{25 \times 3} - \sqrt{9 \times 3} \\ \\ = 5 \sqrt{3} - 3 \sqrt{3} \\ \\ = (5 - 3 )\sqrt{3} \\ \\ =\green{\boxed{ 2 \sqrt{3}}}$