Simplification for IBPS clerk test 5-Solved questions with detailed explanations for SSC, IBPS PO, SBI PO, RRB, RBI, CSE, CGL, CHSL, CDA, CSE, UPSC

6)

What will come in place of question mark (?) in the following questions

$(2 \sqrt{392} - 21) + (\sqrt{8} - 7^{2}) = {(?)}^{2}$

[Corporation Bank (PO), 2009]

A)
4
B)
-4
C)
12
D)
2
E)
6

Answer: Option E

Explanation

$\begin{array}{l} Here, \\ \Rightarrow 2 \sqrt{392} - 21 + (\sqrt{8} - {7)}^{2} {= (?)}^{2} \\ \Rightarrow 2 \sqrt{392} - 21 + 8 + 49 - 14 \sqrt{8} {= (?)}^{2} \\ \Rightarrow \sqrt{4 \times 392} - 21 + 8+ 49 - \sqrt{196 \times 8} \\ {= (?)}^{2} \\ \Rightarrow \sqrt{1568} - 21 + 8 + 49 - \sqrt{1568} {= (?)}^{2} \\ \Rightarrow {(?)}^{2} = 36 \Rightarrow ? = 6 \end{array}$

Hence, Option E is correct.

Discussion

7)

${(94)}^{2} {+ (?)}^{2} {= (145)}^{2} - {(56)}^{2} - 3869$

[UBI (PO), 2009]

A)
5184
B)
72
C)
84
D)
7056
E)
None of these

Answer: Option B

Explanation

$\begin{array}{l} Here, \\ {(?)}^{2} {= (145)}^{2} - {(56)}^{2} - 3869 - {(94)}^{2} \\ {= (145)}^{2} - {{56}^{2} {+ 3869 + (94)}^{2}} \\ {= (145)}^{2} - {3136 + 3869 + 8836} \\ = 21025 - {15841} = 5184 \\ or ? = \sqrt{5184} = 72 \end{array}$

Hence Option B is correct.

Discussion

8)

${(?)}^{3} = 729$

[BOI (PO), 2009]

A)
14
B)
7
C)
19
D)
11
E)
None of these

Answer: Option E

Explanation

$\begin{array}{l} Here, \\ \Rightarrow {(?)}^{3} = 729 \Rightarrow {(?)}^{3} = 9 \times 9 \times 9 \\ \Rightarrow ? = 9 [taking cube root on both sides] \end{array}$

Hence, Option E is correct.

Discussion

9)

${(165)}^{2} + 75 \times {12) + 36 = (?)}^{2}$

[Andhra Bank (PO), 2008]

A)
13
B)
169
C)
121
D)
11
E)
None of these

Answer: Option D

Explanation

$\begin{array}{l} Here, \\ \Rightarrow {(?)}^{2} {= [(165)}^{2} \div 75 \times 12] \div 36 \\ Applying the BODMAS rule, we get \\ \Rightarrow [\frac{165 \times 165}{75} \times 12] \div 36 = ? \\ \Rightarrow [363 \times 12] \div {36 = (?)}^{2} \\ \Rightarrow {(?)}^{2} = \frac{363 \times 12}{36} = 121 \\ \Rightarrow ?= \sqrt{121} =11 \end{array}$

Hence, Option D is correct.

Discussion

10)

$\sqrt{\sqrt{44944} + \sqrt{52441}} =?$

[UBI (PO), 2008]

A)
312
B)
441
C)
485
D)
17
E)
None of these

Answer: Option E

Explanation

$\begin{array}{l} Here, \sqrt{\sqrt{44944} + \sqrt{52441}} =? \\ or ?= \sqrt{212 + 229} = \sqrt{441} \end{array}$

Hence, Option E is correct.

Discussion

Simplification-Test 5 (Based on Square roots and Cube roots/Surds and Indices)

Answer: Option E

Answer: Option B

Answer: Option E

Answer: Option D

Answer: Option E