Answer

Verified

305.1k+ views

**Hint:**First we have to define what the terms we need to solve the problem are. First of all, we just need to know such things about the perfect numbers, which are the numbers that obtain by multiplying any whole number (zero to infinity) twice, or the square of the given number yields a whole number like $\sqrt 9 = 3$ or $9 = {3^2}$.

**Complete step-by-step solution:**

Since the given question is about non-perfect square numbers, there are $2n$ natural numbers that are lying between two consecutive perfect square (as per hint) numbers ${n^2}$ and ${(n + 1)^2}$. so, we will count only natural numbers except for the not perfect squares.

From the given question we have, ${15^2}$ and ${16^2}$, since we can able to write ${16^2}$ as ${(15 + 1)^2}$

Now we will need to find the non-perfect numbers between ${15^2}$ and ${(15 + 1)^2}$, thus $n = 15$ and there are $2n$ natural numbers. now substitute that n in the perfect square equation which is $2(15)$, the natural number for the non-perfect square. Hence further solving we get count $30$ numbers of non-perfect square numbers that are between ${15^2}$ and ${16^2}$

We can also able to solve this problem by comparing the two square numbers and subtracted by one

Which is ${15^2}$,${16^2}$ can be written as ${15^2} = 225$ and ${16^2} = 256$

The formula for this method is $n - m - 1$ (m is the smallest among the both and n is the greater one) and n is always less than m. Hence, we get $n - m - 1 = 256 - 225 - 1$ solving this we get $256 - 225 - 1 = 30$

**Hence there are $30$ non-perfect square numbers between ${15^2}$ and ${16^2}$**

**Note:**Since the equation is about non-perfect square numbers between ${15^2}$ and ${16^2}$, so that only the substrate one occurs $n - m - 1$ if not then like non-perfect square numbers from ${15^2}$ and ${16^2}$, we can simply find by using the $n - m$. So, between is the key for the different formulas.

Recently Updated Pages

The branch of science which deals with nature and natural class 10 physics CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Why is the adrenaline hormone called fight or flight class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between lanthanoids and actinoids class 12 chemistry CBSE

What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.

Give 10 examples of unisexual and bisexual flowers

Open circulatory system is present in I Arthropods class 12 biology CBSE

Name the highest peak of the Indian Himalayas class 8 social science CBSE