Question

Find the square root of a 5 digit number 49abc where a,b,c are non-zero digits such that b=a³=2c.
a. 202
b. 222
c. 122
d. 242​

Answer 1

Answer:

222*222=49284

$8 = {2}^{2} = 2 \times 2$

Answer 2

Concept Introduction :

Multiplying a number by itself will give the original number as a factor.

Given:

A $5$ digit number $49abc$ where $a, b, c$ are non-zero digits such that $b$=$a$³=$2c$.

To Find :

We have to find the square root of the given condition.

Solution:

In mathematics, the number system is the branch that deals with various types of numbers possible to form and easy to operate with different operators such as addition, multiplication and so on.

So, here we are required to find our greatest five-digit natural number. The greatest five-digit natural number is$99999.$

Now considering the greatest five-digit natural number, we will try to evaluate whether it is a perfect square or not.

From the division method of square root evaluation, we get remainder as $143.$

So, this confirms that $99999$ is not a perfect square.

Now, subtracting $143$ from$99999$ we get, $99999$ – $143$ = $99856$.

Hence, $99856$ is the largest five- digit perfect square number.

For finding the square root of $99856$ we could express $99856$ in terms of prime factors as $24$×$792$ and then taking the root, we get the square root of $99856$ as:

$24$×$792$−−−−−−−√$22$²×$79$²=$316$.

Final Answer:

$316$ is the square root

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