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

16)

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

${\sqrt{19683}}_{3} =? \times 3$

[Corporation Bank (PO), 2006]

A)
90
B)
27
C)
3
D)
18
E)
None of these

Answer: Option E

Explanation

$\begin{array}{l} Here, {\sqrt{19683}}_{3} = ? \times 3 \\ \Rightarrow \sqrt{3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3} \\ =? x 3 \\ [∵ 19683=3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3] \\ \Rightarrow {(3}^{9})^{\times \frac{1}{3}} = ? \times 3 \\ \Rightarrow 3^{3} = 3 \times ? \Rightarrow ? = \frac{27}{3} = 9 \end{array}$

Hence Option E is correct.

Discussion

17)

$If \sqrt{80656} = 284, then \sqrt{8.0656} =?$

[United India Insurance Co (AAO), 2002]

A)
28.4
B)
2.84
C)
0.0284
D)
0.284
E)
None of these

Answer: Option B

Explanation

$\begin{array}{l} Here, \sqrt{80656} = 284 \\ \Rightarrow \sqrt{8.0656} = \sqrt{\frac{80656}{10000}} = \frac{284}{100} = 2 .84 \end{array}$

Hence, Option B is correct.

Discussion

18)

$\sqrt{8^{2} \times 7 \times {(5)}^{2} - 175} =?$

[UBI (PO), 2001]

A)
105
B)
95
C)
115
D)
125
E)
None of these

Answer: Option A

Explanation

$\begin{array}{l} Here, \\ \Rightarrow \sqrt{8^{2} \times 7 \times {(5)}^{2} - 175} =? \\ \Rightarrow \sqrt{11200 - 175} = \sqrt{11025} = 105 \end{array}$

Hence, Option A is correct.

Discussion

19)

What will come in place of both the question marks (?) in the following equation?

$\frac{?^{0 .8}}{49} = \frac{189}{?^{2.2}}$

[IBPS (PO), 2014]

A)
18
B)
23
C)
24
D)
21
E)
28

Answer: Option D

Explanation

$\begin{array}{l} Here, put x at the place of ? \\ i . e, \frac{x^{0 .8}}{49} = \frac{189}{?^{2.2}} \\ = x^{0 .8 + 2 .2} = 189 \times 49 \\ [add the power in multiplication] \\ \Rightarrow x^{3} = 189 \times 49 \\ = \frac{27 \times 7 \times 49}{3 \times 3 \times 3 \times 7 \times 7 \times 7} \\ \Rightarrow x = 3 \times 7 = 21 \end{array}$

Discussion

20)

$[(5 \sqrt{7} + \sqrt{7}) \times (4 \sqrt{7} + 8 \sqrt{7})] - {(19)}^{2} = ?$

[IBPS (PO), 2012]

A)
143
B)
img
C)
134
D)
img
E)
None of these

Answer: Option A

Explanation

$\begin{array}{l} Here, \\ [(5 \sqrt{7} + \sqrt{7}) \times (4 \sqrt{7} +8 \sqrt{7}) - {(19)}^{2} = ? \\ \Rightarrow [20 \times 7 + 280 + 28 + 56] - 361 =? \\ \Rightarrow [420 + 84] - 361 =? \\ \Rightarrow 504 - 361 = ? \\ ? = 143 \end{array}$

Hence Option A is correct.

Discussion

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

Answer: Option E

Answer: Option B

Answer: Option A

Answer: Option D

Answer: Option A