Square Root of 165 Simplified

Simplify Square Root Calculator
Simplify the square root of

What is the square root of 165 simplified?

Answer

√165 cannot be simplified — its simplest radical form is
√165

√165 is already in simplest form — 165 has no square factor other than 1, so nothing comes out of the radical. As a decimal, √165 ≈ 12.845.

Simplifying √165 Step by Step

1. Prime factorization. — All Prime Factors of 165:

165 = 3 × 5 × 11

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 factorTimes in 165Comes out of the rootStays under the root
31—3
51—5
111—11

3. Take the pairs out of the root.

√165 = √(3 × 5 × 11)

No prime appears twice, so there is no pair to take out.

√165

4. Check by squaring back.

The only perfect square dividing 165 is 1 = 1², and 1² × 165 = 165

Related Calculations

See Also

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 165 simplified? (The answer is: √165). Enter a whole number (e.g. '165') and hit the 'Simplify' button.
Recalculate with different values ↑

Simplified Square Roots Table

NumberSimplest radical formDecimal value
1505√6≈ 12.247
151√151≈ 12.288
1522√38≈ 12.329
1533√17≈ 12.369
154√154≈ 12.41
155√155≈ 12.45
1562√39≈ 12.49
157√157≈ 12.53
158√158≈ 12.57
159√159≈ 12.61
1604√10≈ 12.649
161√161≈ 12.689
1629√2≈ 12.728
163√163≈ 12.767
1642√41≈ 12.806
165√165≈ 12.845
166√166≈ 12.884
167√167≈ 12.923
1682√42≈ 12.961
1691313
170√170≈ 13.038
1713√19≈ 13.077
1722√43≈ 13.115
173√173≈ 13.153
174√174≈ 13.191
1755√7≈ 13.229
1764√11≈ 13.266
177√177≈ 13.304
178√178≈ 13.342
179√179≈ 13.379

FAQ

What is the square root of 165 simplified?

√165 cannot be simplified — its simplest radical form is √165

Is 165 a perfect square?

No. 165 has no perfect square factor other than 1, so √165 cannot be simplified and stays √165.

What is √165 as a decimal?

√165 ≈ 12.845. The decimal never ends and never repeats, so it is always rounded; the exact value is √165.

What is the largest perfect square that divides 165?

Only 1. 165 has no other square factor, so √165 is already in simplest radical form.

See Also