Question

Simplify :
a. √120 + √180 - √45
b. 2√124 × 5√800 + √3​

Answer 1

Answer:

$a) \sqrt{120} + \sqrt{180} - \sqrt{45}$

$= \sqrt{2 \times 2 \times 2 \times 3 \times 5} + \sqrt{2 \times 2 \times 3 \times 3 \times 5} - \sqrt{3 \times 3 \times 5}$

$= 2 \sqrt{2 \times 3 \times 5} + 2 \times 3 \sqrt{5} - 3 \sqrt{5}$

$= 2 \sqrt{30} + 6 \sqrt{5} - 3 \sqrt{5}$

$= 2 \sqrt{30} + 3 \sqrt{5}$

$b)2 \sqrt{124} \times 5 \sqrt{180} + \sqrt{3}$

$= 2 \sqrt{2 \times 2 \times 31} \times 5 \sqrt{2 \times 2 \times 3 \times 3 \times 5} + \sqrt{3}$

$= 2 \times 2 \sqrt{31} \times 5 \times 2 \times 3 \sqrt{5} + \sqrt{3}$

$= 4 \sqrt{31} \times 30 \sqrt{5} + \sqrt{3}$

$= 120 \sqrt{155} + \sqrt{3}$