Surds And Indices - Study Mode

[#141] Which of the following statement(s) is/are TRUE? $$eqalign{
& { ext{I}}.sqrt {121} + sqrt {12321} + sqrt {1234321} = 1233 cr
& { ext{II}}.sqrt {0.64} + sqrt {64} + sqrt {36} + sqrt {0.36} > 15 cr} $$
Correct Answer

(D) Both I and II

Explanation

Solution: $$eqalign{
& { ext{I}}.sqrt {121} + sqrt {12321} + sqrt {1234321} = 1233 cr
& 11 + 111 + 1111 = 1233 cr
& 1233 = 1233 cr
& { ext{II}}.sqrt {0.64} + sqrt {64} + sqrt {36} + sqrt {0.36} > 15 cr
& frac{8}{{10}} + 8 + 6 + frac{6}{{10}} > 15 cr
& 15.4 > 15 cr
& { ext{Hence statement II is also true}}{ ext{.}} cr} $$

[#142] What is the value of $$sqrt {121} + sqrt {12321} + sqrt {1234321} + sqrt {123454321} ?$$
Correct Answer

(C) 12344

Explanation

Solution: $$eqalign{
& sqrt {121} + sqrt {12321} + sqrt {1234321} + sqrt {123454321} cr
& = 11 + 111 + 1111 + 11111 cr
& = 12344 cr} $$

[#143] The expression $$sqrt {10 + 2left( {sqrt 6 - sqrt {15} - sqrt {10} }
ight)} $$ xa0 xa0xa0 is equal to:
Correct Answer

(A) √3 + √2 - √5

Explanation

Solution: $$eqalign{
& sqrt {10 + 2left( {sqrt 6 - sqrt {15} - sqrt {10} }
ight)} cr
& = sqrt {{{left( {sqrt 2 }
ight)}^2} + {{left( {sqrt 3 }
ight)}^2} + {{left( { - sqrt 5 }
ight)}^2} + 2left( {sqrt 2 imes sqrt 3 - sqrt 3 imes sqrt 5 - sqrt 5 imes sqrt 2 }
ight)} cr
& = sqrt {{{left( {sqrt 2 + sqrt 3 - sqrt 5 }
ight)}^2}} cr
& = sqrt 2 + sqrt 3 - sqrt 5 cr} $$

[#144] Which value among 3 200 , 2 300 and 7 100 is the largest?
Correct Answer

(A) 3 200

Explanation

Solution: 3 200 , 2 300 , 7 100 9 100 , 8 100 , 7 100 It is clear that 3 200 is largest

[#145] If √5 = 2.236, then what is the value of $$frac{{sqrt 5 }}{2} + frac{5}{{3sqrt 5 }} - sqrt {45} ?$$
Correct Answer

(B) -4.845