Question

By what least number should 9075 be multiplied to get a perfect square
number? find the number whose square is the new number.

step by step please​

Answer 1

GivEn:

• Number = 9075

To find:

• The least number it must be multiplied to get a perfect square.

Solution:

• First let's do prime factorization of the given number.

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« Now, Finding prime factors,

• Prime factors are,

→ 9075 = 3 × 5 × 5 × 11 × 11 [ Refer attachment ]

• 5 and 11 are in pairs(2) , 3 is not in any pair.

∴ Thus, We need to multiply the number with 3 to get a perfect square.

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« Now, Finding the new number,

→ The result will be, 27225.

• The new number is,

→ √27225

→ 165

∴ Hence, The new number is 165.

Answer 2

Answer:

165

Step-by-step explanation:

the prime factorization of 9075 is (5^2 × 5^2)×(3^2)×(11^2×11^2)

=5^2×3^2×11^2

=165

hence 165 is the new number