Square Root of 75 Simplified
Simplify Square Root Calculator
What is the square root of 75 simplified?
Answer
√75 = 5√3
75 = 25 × 3, and 25 = 5² is the largest perfect square that divides 75, so √75 = √25 × √3 = 5√3. Check: 5√3 ≈ 8.66, the same as √75 ≈ 8.66.
Simplifying √75 Step by Step
1. Prime factorization. — All Prime Factors of 75:
75 = 3 × 5 × 5 = 3 × 52
2. Pair up equal primes. Each pair is a perfect square and comes out of the root as one factor; a prime without a partner stays under the radical.
| Prime factor | Times in 75 | Comes out of the root | Stays under the root |
|---|---|---|---|
| 3 | 1 | — | 3 |
| 5 | 2 | 5 | — |
3. Take the pairs out of the root.
√75 = √((5 × 5) × 3)
= 5 × √3
= 5√3
4. Check by squaring back.
5² × 3 = 25 × 3 = 75
Related Calculations
See Also
- Square Root Calculator - Calculate the square root of any number
- Factors of a Number - List all Factors and Factor Pairs of a Number
- Prime Number Checker - Find out whether a given number is Prime or not
- Prime Factorization - Prime Factorization Calculator
- Prime Numbers List - List of all Prime Numbers - how many Prime numbers are between
Simplify Square Root Calculator
This calculator writes a square root in simplest radical form: it finds the largest perfect square that divides the number, takes its root out of the radical and leaves the rest under it. For example, it can help you find out what is the square root of 75 simplified? (The answer is: 5√3). Enter a whole number (e.g. '75') and hit the 'Simplify' button.
Simplified Square Roots Table
FAQ
What is the square root of 75 simplified?
√75 = 5√3
Is 75 a perfect square?
No. 75 = 25 × 3: its largest perfect square factor is 25 = 5², and the factor 3 stays under the radical, so √75 = 5√3.
What is √75 as a decimal?
√75 ≈ 8.66. The decimal never ends and never repeats, so it is always rounded; the exact value is 5√3.
What is the largest perfect square that divides 75?
25 = 5². Dividing gives 75 ÷ 25 = 3, and 3 has no square factor left, so √75 = √25 × √3 = 5√3.
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