In each of the following question, find the smallest number by which it should be multiplied to get a perfect square. find the square root of the perfect square so obtained:(a)11,045 (b)11,094
Answers
Answer:
a) number to be multiplied =5 ,resulting square root = 235
b)number to be multiplied = 6,resulting square root = 258
Step-by-step explanation:
a ) prime factorising the number, 11045 = 5×47×47;
that is 11045 = 5 × 47²
if we mutiply another 5 it becomes , 11045 × 5 = 5² ×47²
that is we should multiply 5.
the perfect square will be a 55225
hence √(11045×5) = √55225 = √(5² ×47²)
= 5×47
= 235.
b) prime factorising the number 11094 = 2×3×43×43;
that is 11094 = 2 × 3 × 43²
if we mutiply another 2 and 3 it becomes , 11094 × 2 × 3 = 2×2×3×3 ×43²
= 2²×3²×43²
that is we should multiply 2 × 3 = 6.
the perfect square will be 66564 .
hence √(11094 ×2×3) = √(2²×3² ×43²)
= 2×3×43 =
= 258.
.
Answer:
a) number to be multiplied =5 ,resulting square root = 235
b)number to be multiplied = 6,resulting square root = 258
Step-by-step explanation:
a ) prime factorising the number, 11045 = 5×47×47;
that is 11045 = 5 × 47²
if we mutiply another 5 it becomes , 11045 × 5 = 5² ×47²
that is we should multiply 5.
the perfect square will be a 55225
hence √(11045×5) = √55225 = √(5² ×47²)
= 5×47
= 235.
b) prime factorising the number 11094 = 2×3×43×43;
that is 11094 = 2 × 3 × 43²
if we mutiply another 2 and 3 it becomes , 11094 × 2 × 3 = 2×2×3×3 ×43²
= 2²×3²×43²
that is we should multiply 2 × 3 = 6.
the perfect square will be 66564 .
hence √(11094 ×2×3) = √(2²×3² ×43²)
= 2×3×43 =
= 258.