Squares and Square Roots Test - 3

There are 2n numbers lying between n² and (n + 1)².
Here, n = 1275
n + 1 = 1276
∴ 2n = 2 × 1275 = 2550

Let the number be x.
So, x² - x - 506 = 0
So, x = 23

x² + x² = 900
2x² = 900
x² = 450
x = √450
x = 21.21 m

LCM (2, 4, 8) = 8, but 8 is not a perfect square.
So, the least perfect square which is exactly divisible by 2, 4 and 8 = 16

Value of 1² = 1
Value of 100² = 10000
Therefore, difference = 10000 - 1 = 9999.
So, 9999 natural numbers lie between 1² and 100².

Let the side of the square be x units.
Then, x² = 1296
x = 36 ......................... {Square root of 1296 = 36}

So, one side of square = 36 units

Sum of all the sides = 144 units

Square root of side = 6 units

So, the required ratio = 144/6
= 24 : 1

The given expression: (233)² x (332)² x (444)²
Solve the expression step by step.
Units digit of (233)² = 9 as it has 3 at ones place.
Units digit of (332)² = 4 as it has 2 at ones place.
Units digit of (444)² = 6 as it has 4 at ones place.

Now, we can find the units digit of the given expression by multiplying the ones digits of each part.
9 x 4 x 6 = 216

Therefore, the given expression has 6 at ones place.