model 5 simplifying roots of roots Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 5 EXERCISES
The following question based on power, indices and surds topic of quantitative aptitude
(a) 2
(b) 3
(c) 30
(d) 5
The correct answers to the above question in:
Answer: (b)
Let, x = $√{6+√{6+√{6 +...∞}}}$
On squaring,
$x^2 = 6 + √{6+√{6+√{6 +...∞}}}$
$x^2$ = 6 + x
$x^2$ - x - 6 = 0
$x^2$ - 3x + 2x - 6 = 0
x (x - 3) + 2 (x - 3) = 0
(x + 2) (x - 3) = 0
x = 3 because x ≠ - 2
Using Rule 25
$√{6+√{6+√{6 +...}}}$ = 3
It is because, 6 = 2 × 3 =n (n+1)
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Read more simplifying roots of roots Based Quantitative Aptitude Questions and Answers
Question : 1
Find the value of $√{30+√{30+√{30+...}}}$
a) 6
b) $3√10$
c) 7
d) 5
Answer »Answer: (a)
Let x = $√{30+√{30+√{30+...}}}$
On squaring both sides,
$x^2 = 30+√{30+√{30+√{30+...}}}$
$x^2$ = 30 + x
$x^2$ - x - 30 = 0
$x^2$ - 6x + 5x - 30 = 0
x (x - 6) + 5 (x - 6) = 0
(x - 6) (x + 5) = 0
x = 6 because x ≠ - 5
Using Rule 25
$√{30+√{30+√{30+...}}}$ = 6
It is because
30 = 5 × 6 = n (n +1)
Question : 2
The value of $√{ - √{3}+√{ 3+8√{7 +4√{3}}}}$ is
a) ±2
b) 4
c) - 2
d) 2
Answer »Answer: (d)
Expression
=$√{ - √{3}+√{ 3+8√{7 +4√{3}}}}$
=$√{ - √{3}+√{ 3+8√{4+3+2×2×√{3}}}}$
=$√{ - √{3}+√{ 3+8√{(2)^2+(√3)^2+2×2×√{3}}}}$
=$√{ - √{3}+√{ 3+8√{(2+√3)^2}}}$
=$√{ - √{3}+√{ 3+16+8√3}}$
=$√{ - √{3}+√{(4)^2+(√3)^2+2×4×√3}}$
=$√{ - √{3}+√{(4+√3)^2}}$
=$√{ - √{3}+4+√3}=√4=2$
Question : 3
The value of $√{9 + 2√{ 16} +√^3{ 512}}$ is :
a) $2√8$
b) 5
c) $3√6$
d) 6
Answer »Answer: (b)
Expression
=$√{9 + 2√{16} +√^3{ 512}}$
=$√{9 + 2√{4×4} +√^3{8×8×8}}$
=$√{9 + 2×4+8}$
=$√25$ =5
GET power, indices and surds PRACTICE TEST EXERCISES
model 1 find largest and smallest value
model 2 based on simplification
model 3 based on positive and negative exponent
model 4 simplifying roots with values
model 5 simplifying roots of roots
power, indices and surds Shortcuts and Techniques with Examples
-
model 1 find largest and smallest value
Defination & Shortcuts … -
model 2 based on simplification
Defination & Shortcuts … -
model 3 based on positive and negative exponent
Defination & Shortcuts … -
model 4 simplifying roots with values
Defination & Shortcuts … -
model 5 simplifying roots of roots
Defination & Shortcuts …
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