Question

Square root of 144/225

Answer 1

Answer:

12/15 = 4/5

Step-by-step explanation:

√144/√225

12/15

Answer 2

The square root of $\frac{144}{225}$ is $\frac{12}{15}$.

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 - 144/225

To find :

The square root of 144/225

Solution :

Step 1:

Write the prime factors of 144 and 225

144 =  (2 × 2 × 2 × 2 × 3 × 3)

225 = (5 × 5 × 3 × 3)

Step 2:

Form pair of like factors :

144 = (2 × 2) × ( 2 × 2) × (3 × 3)

225 = (5 × 5) × (3 × 3)

Step 3:

From each pair and pick out one prime factor :

√144 =  2 × 2 × 3

√225 =  5 × 3

Step 4:

Multiply the factors so picked :

The product is the square root of the given number.

√144 =  2 × 2 × 3 = 12

√225 =    5 × 3 = 15

$\sqrt{ \frac{144}{225}} ={ \frac {\sqrt{144}}{\sqrt{225}}} = \frac{12}{15}$

Hence, the square root of $\frac{144}{225}$ is $\frac{12}{15}$.

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