Question

find the prime factorization​ square root of 998001

Answer 1

Answer:

9 |998001

9 |110889

3 |12321

3 |4107

37 |1369

37 |37

now square root =9×3×37=999 Ans

Answer 2

The square root of 998001 by prime factorisation is 999.

Concept used:

Prime factorization method for square roots:

Step 1: Split the given number into prime factors.

Step 2: Form a pair of like factors.

Step 3: From each pair and pick out one prime factor.

Step 4: Multiply the factors so picked.

The product is the square root of the given number.

Given :

Number - 998001

To find :

The square root of 998001 by prime factorisation

Solution :

Step 1:Write the prime factors of 998001

998001 =  (3 × 3 × 3 × 3 × 3 × 3 × 37 × 47)

Step 2:Form pair of like factors :

144 = (3 × 3) × (3 × 3) × (3 × 3) × (37 × 37)

Step 3:From each pair and pick out one prime factor :

√998001 =  3 × 3 × 3 × 37

Step 4:Multiply the factors so picked :

The product is the square root of the given number.

√998001 =  27 × 37

√998001 = 999

Hence, the square root of 998001 is 999.

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