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

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

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New post 10 Aug 2018, 03:20
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

75% (02:03) correct 25% (02:14) wrong based on 154 sessions

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

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New post 10 Aug 2018, 03:36
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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New post 10 Aug 2018, 04:00
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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New post 10 Aug 2018, 04:51
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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New post 10 Aug 2018, 08:06
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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Re: What is the value of (√700 - √112)/√1008  [#permalink]

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New post 11 Aug 2018, 01:38
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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New post 11 Aug 2018, 01:45
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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New post 18 Aug 2018, 20:08
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

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

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New post 19 Aug 2018, 06:35

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.

Answer: E

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Re: What is the value of (√700 - √112)/√1008   [#permalink] 19 Aug 2018, 06:35
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