Question

Find the square root of 4.0401 by prime factorisation method​

Answer 1

To find:

The square root of 4.0401 by prime factorization method.

Solution:

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

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

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

First, let us have a look at the Numerator:

$40401=13467 \times 3\\\Rightarrow 40401=4489 \times 3 \times 3\\\Rightarrow 40401 = 67 \times 67 \times 3 \times 3$

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:

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

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

So, the answer is:

Square root of 4.0401 is 2.01.

Answer 2

Step-by-step explanation:

4.0401

40401÷by 3=13467

13467÷by 3=4489

4489÷by 67=67

67÷by 67=1

pare the numbers you will be left with 3 and 67

=3×67=201 therefore 40401= 201