Question

19600 find the square root by prime factorization with full explanation​

Answer 1

Step-by-step explanation:

this is your answer

please check it

Answer 2

Answer:

Square root of 19600 is 140.

Step-by-step explanation:

Here given number is 19600.

Now what is the square root of 19600.

This is a problem of power of indices.

By prime factorization we can find the answer,

First we need to break 19600 into prime numbers.

$19600 = 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 7 \times 7$

Now,

$\sqrt{19600} = \sqrt{2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 7 \times 7} = 2 \times 2 \times 5 \times 7 = 4 \times 5 \times 7 = 140$

This is a problem of power indices.

Some formulas of power indices,

${x}^{0} = 1 \\ {x}^{1} = x \\ {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ {x}^{ {y}^{a} } = {x}^{ya} \\ {x}^{ - 1} = \frac{1}{x} \\ {x}^{a} \times {y}^{a} = {(xy)}^{a}$