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# What is the value of (√700 - √112)/√1008

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Joined: 02 Sep 2009
Posts: 52294
What is the value of (√700 - √112)/√1008  [#permalink]

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10 Aug 2018, 02:20
00:00

Difficulty:

25% (medium)

Question Stats:

81% (01:32) correct 19% (02:10) wrong based on 129 sessions

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What is the value of $$\frac{√700 - √112}{√1008}$$?

A. √15/√34

B. 1/4

C. 1/3

D. √157/(6√6)

E. 1/2

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Re: What is the value of (√700 - √112)/√1008  [#permalink]

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10 Aug 2018, 02:36
1
Bunuel wrote:
What is the value of $$\frac{√700 - √112}{√1008}$$?

A. √15/√34

B. 1/4

C. 1/3

D. √157/(6√6)

E. 1/2

Nearest perfect of 700 is 696=$$26^2$$
Nearest perfect of 112 is 100=$$10^2$$
Nearest perfect of 1008 is 961=$$31^2$$

Now, $$\frac{√700 - √112}{√1008}$$=$$\frac{26-10}{31}=\frac{16}{31}=\frac{1}{2}$$(Approx)

Ans. (E)
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Re: What is the value of (√700 - √112)/√1008  [#permalink]

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10 Aug 2018, 03:00
2
Bunuel wrote:
What is the value of $$\frac{√700 - √112}{√1008}$$?

A. √15/√34

B. 1/4

C. 1/3

D. √157/(6√6)

E. 1/2

((10√7) - (4√7))/(12√7)
= 6√7/12√7 = 1/2

Hence E

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Re: What is the value of (√700 - √112)/√1008  [#permalink]

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10 Aug 2018, 03:51
Bunuel wrote:
What is the value of $$\frac{√700 - √112}{√1008}$$?

= √700 - √112 / √1008
= ( √7*100 - √7*16 ) / ( √7*144 )
= ( 10√7 - 4√7 ) / 12√7
= 6√7 / 12√7
= 1 / 2

Hence, E.
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Re: What is the value of (√700 - √112)/√1008  [#permalink]

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10 Aug 2018, 07:06
1
Bunuel wrote:
What is the value of $$\frac{√700 - √112}{√1008}$$?

A. √15/√34

B. 1/4

C. 1/3

D. √157/(6√6)

E. 1/2

$$\frac{√700 - √112}{√1008}$$

= $$10\sqrt{7} - 4\sqrt{7}/12\sqrt{7}$$

= $$3\sqrt{7}/12\sqrt{7}$$

=$$\frac{1}{4}$$, Answer must be (B)
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Posts: 260
Re: What is the value of (√700 - √112)/√1008  [#permalink]

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11 Aug 2018, 00:38
1
Bunuel wrote:
What is the value of $$\frac{√700 - √112}{√1008}$$?

A. √15/√34

B. 1/4

C. 1/3

D. √157/(6√6)

E. 1/2

OA:E

$$\frac{\sqrt{700}-\sqrt{112}}{\sqrt{1008}}$$

$$=\frac {\sqrt{7*10^2}-\sqrt{7*4^2}}{\sqrt{7*12^2}}$$

$$=\frac {10\sqrt{7}-4\sqrt{7}}{12\sqrt{7}}=\frac {6\sqrt{7}}{12\sqrt{7}}=\frac{6}{12}=\frac{1}{2}$$
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What is the value of (√700 - √112)/√1008  [#permalink]

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11 Aug 2018, 00:45
Abhishek009 wrote:
Bunuel wrote:
What is the value of $$\frac{√700 - √112}{√1008}$$?

A. √15/√34

B. 1/4

C. 1/3

D. √157/(6√6)

E. 1/2

$$\frac{√700 - √112}{√1008}$$

= $$10\sqrt{7} - 4\sqrt{7}/12\sqrt{7}$$

= $$3\sqrt{7}/12\sqrt{7}$$

Shouldn't it be 6 instead of 3?
=$$\frac{1}{4}$$, Answer must be (B)

I think the yellow part leads to the wrong result
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Re: What is the value of (√700 - √112)/√1008  [#permalink]

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18 Aug 2018, 19:08
Bunuel wrote:
What is the value of $$\frac{√700 - √112}{√1008}$$?

A. √15/√34

B. 1/4

C. 1/3

D. √157/(6√6)

E. 1/2

√700 = √100 x √7 = 10√7

√112 = √16 x √7 = 4√7

√1008 = √144 x √7 = 12√7

So we have:

(10√7 - 4√7)/12√7

6√7/12√7

6/12

1/2

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Re: What is the value of (√700 - √112)/√1008  [#permalink]

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19 Aug 2018, 05:35

Solution

To find:
The value of $$\frac{\sqrt{700}-\sqrt{112}} {\sqrt{1008}}[/fraction]$$

Approach and Working:
• $$\frac{\sqrt{700}-\sqrt{112}} {\sqrt{1008}}$$= $$\frac{\sqrt{7*100}- \sqrt{7*16}}{\sqrt{16*9*7}}$$
• $$\frac{10 \sqrt{7} – 4 \sqrt{7}}{12 \sqrt{7}}$$
• =$$\frac{6 \sqrt{7}} {12 \sqrt{7}}$$
• =$$\frac{1}{2}$$

Hence, the correct answer is option E.

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Re: What is the value of (√700 - √112)/√1008 &nbs [#permalink] 19 Aug 2018, 05:35
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