Problem Solving

boomgoesthegmat wrote:√80 + √125 =

A) 9sqrt(5)
B) 20sqrt(5)
C) 41sqrt(5)
D) sqrt(205)
E) 100

OA: A

IMPORTANT RULE: √(xy) = (√x)(√y)

So, √80 + √125 = √(16 x 5) + √(25 x 5)
= (√16)(√5) + (√25)(√5)
= 4√5 + 5√5
= 9√5
= A

Related Resource
The following video covers the concepts/strategies that are useful for answering this question:
- Simplifying roots: https://www.gmatprepnow.com/module/gmat ... video/1038


Cheers,
Brent

boomgoesthegmat wrote:√80 + √125 =

A) 9sqrt(5)
B) 20sqrt(5)
C) 41sqrt(5)
D) sqrt(205)
E) 100

OA: A

Another approach is to ESTIMATE

We know that √81 = 9, so √80 is a little bit less than 9
We know that √121 = 11, so √125 is a little bit more than 11

So, √80 + √125 ≈ 9 + 11 ≈ 20

When we check the answer choices, we must keep in mind that √5 ≈ 2.2

A) 9√5 ≈ (9)(2.2) ≈ 20 NICE!!
B) 20√5 ≈ (20)(2.2) ≈ 44 NO GOOD. ELIMINATE
C) 41√5 ≈ (20)(2.2) ≈ TOO BIG. ELIMINATE
D) √205. We know that √225 = 15. So, √205 is too small. ELIMINATE
E) 100 ELIMINATE

Answer: B

Cheers,
Brent

boomgoesthegmat wrote:sqrt(80) + sqrt(125) =

A) 9sqrt(5)
B) 20sqrt(5)
C) 41sqrt(5)
D) sqrt(205)
E) 100

√80 = √16 x √5 = 4√5

√125 = √25 x √5 = 5√5

Now we can add these two results together:

4√5 + 5√5 = 9√5

Answer: A

Hi All,

We're asked for the value of √80 + √125. This question comes down to some standard Radical rules (which you will likely be asked to use 1-2 times on Test Day).

You likely already know a number of perfect squares already (1, 4, 9, 16, 25, etc.), so you can square-root each of those numbers too. When a prompt gives you a radical that is NOT a perfect square, a good 'first step' is often to try to break that radical into 'pieces' (with one of the pieces being a perfect square).

With √80, we can rewrite that value as √(5)(16)...
and then 'pull out' the 16, giving us 4√5

We can do the same thing with the √125.... √(5)(25)...
and then 'pull out' the 25, giving us 5√5

Thus, the sum of those two values is...
4√5 + 5√5 = 9√5

Final Answer: A

GMAT assassins aren't born, they're made,
Rich