Mathematics Short Tricks/ SQUARE ROOT Tricks for Placement tricks.

Diznr International

2 months ago

Contents

The square root of a number x is a number y such that $y^2 = x$ .
Example:
$25=5\sqrt{25} = 5$ because $5^2 = 25$ .

If the number is a perfect square, simply find its square root.

Estimate between which two perfect squares the number lies.

Example: $50\sqrt{50}$ lies between $7^2 = 49$ and $8^2 = 64$ .
Approximate value: 7.1 or 7.2

Used for precise square root calculation for large numbers.

Example: $324\sqrt{324}$
Divide the number into pairs from right to left: 3 | 24
Try $1$ (1 × 1 = 1) → Subtract (3 – 1 = 2) → Bring down 24 → Try 8 (28 × 8 = 224)
Answer: 18

Perfect squares end in 0, 1, 4, 5, 6, 9. Use this to find the square root.

Example: Find $784\sqrt{784}$
Last digit 4 means root ends in 2 or 8.
$28^2 = 784$ ⇒ Answer: 28

Use the formula:
$(a2+b)≈a+b2a\sqrt{(a^2 + b)} \approx a + \frac{b}{2a}$
where $a$ is the nearest perfect square root and $b$ is the difference.

Example: $47\sqrt{47}$
Nearest perfect square = 49 (7²)
$49 - 47 = 2$
$47≈7−214=7−0.14=6.86\sqrt{47} \approx 7 – \frac{2}{14} = 7 – 0.14 = 6.86$

To find the square root of decimals, make pairs from the decimal point.

Example: $0.0049\sqrt{0.0049}$
Pairs: $49$ — Square root of 49 is 7
Decimal places = 4, so square root will have 2 decimal places.
Answer: 0.07

If you need more detailed methods or have specific questions, just let me know!