Question

find the square root by prime factorization 4.0401​

Answer 1

Answer:

900=√2*2*5*5*3*3=2*5*3=30. (Ans.) Therefore the square root of 900 is 30. Hope it helps you

Answer 2

Step-by-step explanation:

To find:

The square root of 4.0401 by prime factorization method.

Solution:

First of all, let us write the given number in \frac{p}{q}

q

p

form.

4.0401 = \dfrac{40401}{10000}4.0401=

10000

40401

Now, let us factorize numerator and denominator separately with prime numbers.

First, let us have a look at the Numerator:

$$\begin{lgathered}40401=13467 \times 3\\\Rightarrow 40401=4489 \times 3 \times 3\\\Rightarrow 40401 = 67 \times 67 \times 3 \times 3\end{lgathered}$$

Now, let us make pairs:

$$40401 =\underline {67\times 67} \times \underline {3 \times 3}$$

$$\Rightarrow \sqrt{40401} = 67 \times 3 = 201$$

Now, similarly let us have a look at the denominator:

$$\begin{lgathered}10000 = \underline {2 \times 2 \times}\times \underline{2 \times 2}\times \underline{5 \times 5}\times \underline{5 \times 5}\\\Rightarrow \sqrt{10000} = 2 \times 2 \times 5\times 5 = 100\end{lgathered}$$

$$\therefore \sqrt{4.0401} = \sqrt{\dfrac{40401}{10000}} = \dfrac{201}{100} = 2.01$$

So, the answer is:

Square root of 4.0401 is 2.01.