Question

Simplify:
2√30/√6-3√140/√28+√55/√99​

Answer 1

Answer:

$- 2 \sqrt{5} \div 3$

Step-by-step explanation:

$2 \sqrt{30 } \div \sqrt{6 - 3} \sqrt{140} \div \sqrt{28} + \sqrt{55} \div \sqrt{99 = }$

$(2 \sqrt{5} \times \sqrt{6} \sqrt{6}) \: - (3 \sqrt{5} \times \sqrt{28} \div \sqrt{28} ) + ( \sqrt{11} \times \sqrt{5} \div \sqrt{11} \times \sqrt{9)}$

( cancel)

$(2 \sqrt{5} ) - (3 \sqrt{5} ) + ( \sqrt{5 } \div \sqrt{9} )$

$2 \sqrt{5} - 3 \sqrt{5} + \sqrt{5} \div 3$

$(2 - 3) \sqrt{5} + ( \sqrt{5} \div 3)$

( common = √ 5)

$1 \sqrt{5} + \sqrt{5} \div 3$

$3 \sqrt{5} + \sqrt{5} \div 3 \: \: \: (take \: lcm \: 3)$

$( - 3 + 1) \sqrt{5} \div 3$

$- 2 \sqrt{5} \div 3$