Question

plz answer 2.bit questions ​

Answer 1

Answer:

1. First of all find the prime factors of the given numbers.

2. Arrange the factors in pairs such that the two primes in each pair are equal.

3. Take one number from each pair and multiply all such numbers.

4. The product obtained in step 3 is the required square root of the given number. ___________________________________----------------------------------------------------------------

1.) 425

First find the prime factors of 425 by prime factorization.

Hence,

425 = 5 × 5 × 17

= (5 ×5) × 17

Hence, we see that 5 occurs in pair but 17 needs a pair. Hence the given number is not a perfect square.

If we now multiply 425 by 17 then we get

425 × 17 = 7225 = (5 × 5) × (17 × 17)

Therefore the number 425 has 2 pairs of equal prime factors.

Hence, 7225 is a perfect square and √7225 = 5 × 17 = 85

Hence the smallest number by which 7225 must be multiplied so that the product is a perfect square is 17.

And the square root of the new number is √7225 = 85 ___________________________________------------------------------------------------------------------

2.) 500

By prime factorization we get

500 = 2 × 2 × 5 × 5 × 5

= (2×2) × (5×5) × 5

Hence we see that 2 and 5 occurs in pair but other 5 needs a pair to make 500 a perfect square.

If we multiply 500 by 5 we get

500 × 5 = 2500 = (2×2) × (5×5) × (5×5)

Therefore the number 500 has three pairs of equal prime factors.

Hence 2500 is a perfect square and √2500 = 2 × 5 × 5

Hence the samllest number by which 2500 must be multiplied so that the product is a perfect square is 5.

And the square root of the new number is√2500 = 50 ___________________________________------------------------------------------------------------------

3.) 2352

By prime factorization we get

2352 = 2 × 2 × 2 × 2 × 7 ×7 × 3

= (2×2) × (2×2) × (7×7) × 3

Hence we see that 2 and 7 occurs in pair but 3 needs a pair to make 2352 a perfect square.

If we multiply 2352 by 3 we get

2352 × 3 = 7056 = (2×2) × (2×2) ×(7×7) × (3×3)

Therefore the number 2352 has four pairs of equal prime factors.

Hence 7056 is a perfect square and√7056 = 2× 2 × 7 × 3

Hence the samllest number by which 7056 must be multiplied so that the product is a perfect square is 3.

And the square root of the new number is √7056 = 84 ___________________________________------------------------------------------------------------------

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