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# sqrt(9*15+5*18)=?

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Updated on: 23 Apr 2017, 04:55
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Difficulty:

5% (low)

Question Stats:

81% (01:15) correct 19% (02:07) wrong based on 164 sessions

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$$\sqrt{9\times 15 + 5 \times 18} =$$

A. $$3\sqrt{20}$$
B. $$15$$
C. $$25$$
D. $$3\sqrt{20}+3\sqrt{10}$$
E. $$34$$

Source: GMAT Free

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Originally posted by broall on 22 Apr 2017, 07:12.
Last edited by broall on 23 Apr 2017, 04:55, edited 1 time in total.
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22 Apr 2017, 07:31
sqrt(9*15+5*18)

---> 3 sqrt(15+5*2)
---->3*5
----->15
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22 Apr 2017, 09:40
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nguyendinhtuong wrote:
$$\sqrt{9\times 15 + 5 \times 18} =$$

A. $$3\sqrt{20}$$
B. $$15$$
C. $$25$$
D. $$3\sqrt{20}+3\sqrt{10}$$
E. 34

Factor everything:

$$\sqrt{3*3*3*5 + 5*2*3*3}$$

Notice you can factor out a 9:

= $$\sqrt{9 * (15 + 10)}$$

= $$\sqrt{(9)(25)}$$

= $$\sqrt{9}$$ * $$\sqrt{25}$$

= 3 * 5 = 15. Answer B
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22 Apr 2017, 09:49
nguyendinhtuong wrote:
$$\sqrt{9\times 15 + 5 \times 18} =$$

A. $$3\sqrt{20}$$
B. $$15$$
C. $$25$$
D. $$3\sqrt{20}+3\sqrt{10}$$
E. 34

sqrt(9*15+5*18)
= sqrt(135+90)
=sqrt(225)
=15

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23 Apr 2017, 05:35
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nguyendinhtuong wrote:
$$\sqrt{9\times 15 + 5 \times 18} =$$

A. $$3\sqrt{20}$$
B. $$15$$
C. $$25$$
D. $$3\sqrt{20}+3\sqrt{10}$$
E. $$34$$

There's a useful rule that says: AB = (2A)($$\frac{1}{2}$$B) [for more on this, see video below]
So (5)(18) = (10)(9)

We get: √(9 x 15 + 5 x 18) = √(9 x 15 + 10 x 9)
= √[9(15 + 10)]
= √[(9)(25)]
= (√9)(√25)
= (3)(5)
= 15

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23 Mar 2018, 00:31
broall wrote:
$$\sqrt{9\times 15 + 5 \times 18} =$$

A. $$3\sqrt{20}$$
B. $$15$$
C. $$25$$
D. $$3\sqrt{20}+3\sqrt{10}$$
E. $$34$$

Source: GMAT Free

$$\sqrt{9\times 15 + 5 \times 18} =$$

Factor out 9,

$$\sqrt{9(15 + 5*2)}$$

$$\sqrt{9 * 25}$$

3 * 5

15 (B)
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26 Mar 2018, 17:43
broall wrote:
$$\sqrt{9\times 15 + 5 \times 18} =$$

A. $$3\sqrt{20}$$
B. $$15$$
C. $$25$$
D. $$3\sqrt{20}+3\sqrt{10}$$
E. $$34$$

We see that 9 is a common factor of both (9 x 15) and (5 x 18). Simplifying, we have:

√[9 x (15 + 5 x 2)]

√(9 x 25)

√9 x √25

3 x 5

15

Alternate Solution:

√(9 x 15 + 5 x 18)] = √(135 + 90) = √225 = 15

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Re: sqrt(9*15+5*18)=?   [#permalink] 26 Mar 2018, 17:43
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