Question

what are the possible numbers of a digit in a square of a two digit number​

Answer 1

Step-by-step explanation:

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MATHS

How many digits are possible in the square of a 'n' digit number?

THIS QUESTION HAS MULTIPLE CORRECT OPTIONS

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ANSWER

Let us consider 1st number as 1

No. of digit : 1

Square : 1

2

=1

No. of digit in square = 1

satisfying options (B) and (C)

Now let us consider 2nd number as 4

No. of digit : 1

Square : 4

2

=16

No. of digit in square = 2

satisfying options (D)

If we take 3rd number as 25

No. of digit : 2

Square : 25

2

=625

No. of digit in square = 3

Answer 2

Solution

The smallest 2-digit number is ten.

The smallest 3-digit number is one hundred.

Now, two-digit numbers can be written in this mathematic phrase:-

$\sf{10\leq k<100}$ (where k are natural numbers)

Now, this can be divided into two phrases:-

• $\sf{10\leq k}$ ...(1)
• $\sf{k<100}$ ...(2)

We obtain:-

• $\sf{100\leq k^2}$ From (1)
• $\sf{k^2<10000}$ From (2)

Now:-

$\sf{\therefore{100\leq k<10000}}$

$\sf{\therefore{10^2\leq k<10^4}}$

Therefore, possible digits are 3 or 4

since the exponents denote the digits 1 less.

Underlying Concepts

• Inequality
• Exponent: That exponent of 10 shows the digits 1 less.