Question

Simplify:

3√45 - √125 + √200 - √50

2√30/√6 - 3√140/√28 + √55/√99

√72 + √800 - √18

Answer 1

√72 - √800 - √18
= √36×2 - √400×2 - √9×2
= 6√2 - 20√2 - 3√2
= (6 - 20 - 3)√2
= (-14 - 3)√2
= -17√2

The answer is -17√2

Consider, 3√45-√125+√200-√50
= 3 √(9 × 5) − √(25 × 5) + √(100 × 2) − √(25 × 2)
= 9√5 − 5√5 + 10√2 − 5√2
= 4√5 + 5√2





Consider
(2√30/√6) - (3√140/√28) + (√55/√99)

=(2√5×√6/√6) - ( 3√5×√28/√28) + (√11×√5/√11×√9)


= (2√5) - (3√5) + (√5/√9)

= 2√5 - 3√5 + (√5/3)

= (2-3)√5 + (√5/3)

(take common as √5)

= -1√5 + (√5/3)

(LCM OF 1 and 3 is 3)

= (-3√5+√5)/3

= (-3+1)√5/3

(take common as √5)

= -2√5/3