If a > b > 0, then a^2 - b^2

[m]\sqrt{a + b},\sqrt{a - b}[/m]

Free Practice Question

PS · Problem Solving

sub-505

Roots

If $a > b > 0$ , then $\sqrt{a^2 - b^2}$

Correct answer marked below

\sqrt{a + b - 2ab}

\sqrt{a - b + 2ab}

\sqrt{(a - b)^2 - 2ab}

\sqrt{a + b},\sqrt{a - b}

Correct

(\sqrt{a} + \sqrt{b})(\sqrt{a} - \sqrt{b})

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Explanation

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Comments

PrabalJun 7

thanks, easy points. factoring is the move here

SukanayaJun 17

which factoring exactly? i keep getting stuck on (D)

BebasJul 19

wait is D written as a product of two radicals? the comma is confusing me lol

TeddyJul 27

yea it's a product, the comma is just a typo. read it as sqrt(a+b) times sqrt(a-b)

LakshyaAug 7

got it in like 30 sec. a>b>0 just means both factors are positive so no sign issues

LoaiMay 4

ngl I stared at the answer choices longer than the actual math. (D) looked weird but once you multiply the two radicals back it makes sense

What this question tests

Your handling of square and higher roots, including simplifying radicals.

Forgetting the ± when taking a square root to solve an equation, or assuming √(a²) = a.