19 Search

Q:

If $a = \frac{\sqrt{5} + 1}{\sqrt{5} - 1} b = \frac{\sqrt{5} - 1}{\sqrt{5} + 1} t h e n f i n d t h e v a l u e o f [\frac{a^{2} + a b + b^{2}}{a^{2} - a b + b^{2}}] i s : :$

A) 3/4	B) 4/3
C) 3/5	D) 5/3

Answer & Explanation Answer: B) 4/3

Explanation:

By simplifying, we get 4/3

Report Error

View Answer Report Error Discuss

Filed Under: Square Roots and Cube Roots
Exam Prep: AIEEE , Bank Exams , CAT
Job Role: Bank Clerk , Bank PO

Q:

If x = $7 - 4 \sqrt{3} t h e n f i n d t h e v a l u e o f (x + \frac{1}{x}) ?$

A) 3sqrt{3}	B) 8sqrt{3}
C) 14	D) 14+8sqrt{3}

Answer & Explanation Answer: C) 14

Explanation:

Report Error

View Answer Report Error Discuss

Filed Under: Square Roots and Cube Roots
Exam Prep: Bank Exams , CAT
Job Role: Bank Clerk , Bank PO

Q:

$\frac{3 + \sqrt{6}}{5 \sqrt{3} - 2 \sqrt{12} - \sqrt{30} + \sqrt{50}} = ?$

A) 3	B) 3sqrt{2}
C) 6	D) None of these

Answer & Explanation Answer: D) None of these

Explanation:

Report Error

View Answer Report Error Discuss

Filed Under: Square Roots and Cube Roots
Exam Prep: AIEEE , Bank Exams , CAT
Job Role: Bank Clerk , Bank PO

Q:

If $\frac{5 + 2 \sqrt{3}}{7 + 4 \sqrt{3}} = a + b \sqrt{3} t h e n a & b = ?$

A) a=-11,b=-6	B) a=-11,b=6
C) a=11,b=-6	D) a=11,b=6

Answer & Explanation Answer: C) a=11,b=-6

Explanation:

Report Error

View Answer Report Error Discuss

Filed Under: Square Roots and Cube Roots
Exam Prep: AIEEE , Bank Exams , CAT
Job Role: Bank Clerk , Bank PO

Q:

$[\frac{3 \sqrt{2}}{\sqrt{6} - \sqrt{3}} - \frac{4 \sqrt{3}}{\sqrt{6} - \sqrt{2}} - \frac{6}{\sqrt{8} - \sqrt{12}}] = ?$

A) sqtr{3}-sqrt{2}	B) sqtr{3}+sqrt{2}
C) 5sqrt{3}	D) 1

Answer & Explanation Answer: C) 5sqrt{3}

Explanation:

Given Exp = $\frac{3 \sqrt{2}}{\sqrt{6} - \sqrt{3}} \times \frac{\sqrt{6} + \sqrt{3}}{\sqrt{6} + \sqrt{3}} - \frac{4 \sqrt{3}}{\sqrt{6} - \sqrt{2}} \times \frac{\sqrt{6} + \sqrt{2}}{\sqrt{6} + \sqrt{2}} - \frac{6}{2 (\sqrt{2} - \sqrt{3})}$

= $\frac{3 \sqrt{2} (\sqrt{6} + \sqrt{3})}{6 - 3} - \frac{4 \sqrt{3} (\sqrt{6} + \sqrt{2})}{6 - 2} + \frac{3}{(\sqrt{3} - \sqrt{2})} \times \frac{(\sqrt{3} + \sqrt{2})}{(\sqrt{3} + \sqrt{2})}$

= $\sqrt{2} (\sqrt{6} + \sqrt{3}) - \sqrt{3} (\sqrt{6} + \sqrt{2}) + 3 (\sqrt{3} + \sqrt{2})$

= $\sqrt{12} + \sqrt{6} - \sqrt{18} - \sqrt{6} + 3 \sqrt{3} + 3 \sqrt{2}$

= $5 \sqrt{3}$

Report Error

View Answer Report Error Discuss

Filed Under: Square Roots and Cube Roots

Q:

If 3a=4b=6c and $a + b + c = 27 \sqrt{29}$ , then $\sqrt{a^{2} + b^{2} + c^{2}} = ?$

A) 81	B) 83
C) 87	D) None of these

Answer & Explanation Answer: C) 87

Explanation:

$4 b = 6 c \Rightarrow b = \frac{3}{2} c a n d 3 a = 4 b \Rightarrow a = \frac{4}{3} b = \frac{4}{3} (\frac{3}{2} c) = 2 c$

$a + b + c = 27 \sqrt{29} \Rightarrow 2 c + \frac{3}{2} c + c = 27 \sqrt{29} \Rightarrow c = 6 \sqrt{29}$

$∴ \sqrt{a^{2} + b^{2} + c^{2}} = \sqrt{(a + b + b)^{2} - 2 (a b + b c + c a)}$

$= \sqrt{(27 \sqrt{29})^{2} - 2 (2 c \times \frac{3}{2} c + \frac{3}{2} c \times c + c \times 2 c)}$

$= \sqrt{(729 \times 29) - 2 \times \frac{13}{2} c^{2}}$

= 87

Report Error

View Answer Report Error Discuss

Filed Under: Square Roots and Cube Roots

Q:

$\sqrt{(\frac{(0.75)^{3}}{1 - 0.75} + [0.75 + {(0.75)}^{2} + 1])} = ?$

A) 1	B) 2
C) 3	D) 4

Answer & Explanation Answer: B) 2

Explanation:

$\sqrt{(\frac{(0.75)^{3}}{1 - 0.75} + [0.75 + (0.75)^{2} + 1])} = \sqrt{\frac{(0.75)^{3} + (1 - 0.75) [(1)^{2} + (0.75)^{2} + 1 \times 0.75]}{1 - 0.75}}$

= $\sqrt{\frac{(0.75)^{3} + [(1)^{3} - (0.75)^{3}]}{1 - 0.75}} = \sqrt{\frac{1}{0.25}} = \sqrt{4} = 2$

Report Error

View Answer Report Error Discuss

Filed Under: Square Roots and Cube Roots

Q:

$\sqrt{\frac{0.204 \times 42}{0.07 \times 3.4}}$ is equal to:

A) 1/6	B) 0.06
C) 0.6	D) 6

Answer & Explanation Answer: D) 6

Explanation:

$\sqrt{\frac{0.204 \times 42}{0.07 \times 3.4}} = \sqrt{\frac{8568}{238}} = \sqrt{36} = 6$

Report Error

View Answer Report Error Discuss

Filed Under: Square Roots and Cube Roots

Searching for "19"

Quick Links