Question

simplify 1/2+√5+1/√5+√6+1/√6+√7+1/√7+√8

Answer 1

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Answer 2

Answer:

$\frac{1}{\sqrt{5}+2}+\frac{1}{\sqrt{6}+\sqrt{5}}+\frac{1}{\sqrt{7}+\sqrt{6}}+\frac{1}{\sqrt{8}+\sqrt{7}}$ = 2(√2-1)

Solution:

Find the LCM for the denominators and simplify the above set of expression

After taking lcm we get the expression as

=(√5-2)+ (√6-√5)+ (√7-√6)+ (√8-√7)

Multiply the + into the brackets for further simplification

=√5-2+ √6-√5+ √7-√6 + √8-√7

= √8-2

=2√2-2                               [where 8 can be written as 2√2]

Taking the common terms

=2(√2-1)

Hence simplified

Simplification a process or procedure for the reducing the expanded expression or equation into simpler set of numbers