Question

if the unit digit of a perfect square number is 9 then what will be the unit digit of its square root?​

Answer 1

Answer:

3 or 7

Step-by-step explanation:

See if the unit digit of a square number is 9,

Unit digit after numbers square root will be 3 or 7

Example:

1. 3^2 = 9 when we take square root we get 3
2. 7^2 = 49 when we take square root we get 7
3. 23^2 = 529, after root we get 23, unit digit 3
4. 27^2 = 729, after root we get 27, unit digit 7

Thus unit digit can be 3 or 7

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Answer 2

Given,

The unit digit of a perfect square number is 9.

To find,

The unit digit of the square root of that perfect square number.

Solution,

Since, the 9 is at the unit place of the perfect square number, then we need to focus on the calculations of the unit digit only. Because, when we will square the number the unit digit will multiply with itself to produce 9 and no more addition work will take place.

So, we just need to find the digits which will produce 9 at the unit place, when we square them.

First digit = 3

By squaring = 3×3 = 9

Second digit = 7

By squaring = 7×7 = 49

So, the unit digit of the square root will be 7 or 3.

Verification :

1. 289 is a perfect square with 9 at the unit place. By square rooting we get 17, which has 7 at the unit place.
2. 169 is also a perfect square with 9 at the unit place. By square routing we get 13 which has 3 at the unit place.

Hence, the unit digit will be either 7 or 3.