Simplification
- Number of digits in the square root of 62478078 is:
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Number of digits in 62478078 = 8
∴ Number of digits in its square root = 4
⇒ √62478078 ≈ 7904
⇒ √62473216 = 7904Correct Option: A
Number of digits in 62478078 = 8
∴ Number of digits in its square root = 4
⇒ √62478078 ≈ 7904
⇒ √62473216 = 7904
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The simplified value of √32 + √48 is √8 + √12
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Expression = √32 + √48 √8 + √12 = 4√2 + 4√3 = 4(√2 + √3) = 2 2√2 + 2√3 2(√2 + √3) Correct Option: B
Expression = √32 + √48 √8 + √12 = 4√2 + 4√3 = 4(√2 + √3) = 2 2√2 + 2√3 2(√2 + √3)
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Simplify : √ 3 33 ÷ √ 9 1 × 2 √ 3 1 64 7 9
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Expression = √ 3 33 ÷ √ 9 1 × 2 √ 3 1 64 7 9 = √ 225 ÷ √ 64 × 2 √ 28 64 7 9 = √ 25 × 7 × 28 × 2 64 64 9 = 5 × 7 × 2 = 35 = 2 3 8 × 4 16 16 Correct Option: D
Expression = √ 3 33 ÷ √ 9 1 × 2 √ 3 1 64 7 9 = √ 225 ÷ √ 64 × 2 √ 28 64 7 9 = √ 25 × 7 × 28 × 2 64 64 9 = 5 × 7 × 2 = 35 = 2 3 8 × 4 16 16
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What is the value of √24 + √216 ? √96
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Expression = √24 + √216 √96 = 2√6 + 6√6 = 8√6 = 2 4√6 4√6 Correct Option: C
Expression = √24 + √216 √96 = 2√6 + 6√6 = 8√6 = 2 4√6 4√6
- The number of pairs of natural numbers, the difference of whose squares is 45 will be
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Let the numbers be x and y where x > y
∴ x2 − y2 = 45
⇒ (x + y)(x – y) = 45
Now, 45 = 5 × 9
= 15 × 3 = 45 × 1
∴ Number of pairs = 3Correct Option: B
Let the numbers be x and y where x > y
∴ x2 − y2 = 45
⇒ (x + y)(x – y) = 45
Now, 45 = 5 × 9
= 15 × 3 = 45 × 1
∴ Number of pairs = 3