Square Root of 153 Simplified

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What is the square root of 153 simplified?

Answer

√153 = 3√17

153 = 9 × 17, and 9 = 3² is the largest perfect square that divides 153, so √153 = √9 × √17 = 3√17. Check: 3√17 ≈ 12.369, the same as √153 ≈ 12.369.

Simplifying √153 Step by Step

1. Prime factorization. — All Prime Factors of 153:

153 = 3 × 3 × 17 = 32 × 17

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 153Comes out of the rootStays under the root
323—
171—17

3. Take the pairs out of the root.

√153 = √((3 × 3) × 17)

= 3 × √17

= 3√17

4. Check by squaring back.

3² × 17 = 9 × 17 = 153

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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 153 simplified? (The answer is: 3√17). Enter a whole number (e.g. '153') and hit the 'Simplify' button.
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Simplified Square Roots Table

NumberSimplest radical formDecimal value
138√138≈ 11.747
139√139≈ 11.79
1402√35≈ 11.832
141√141≈ 11.874
142√142≈ 11.916
143√143≈ 11.958
1441212
145√145≈ 12.042
146√146≈ 12.083
1477√3≈ 12.124
1482√37≈ 12.166
149√149≈ 12.207
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

FAQ

What is the square root of 153 simplified?

√153 = 3√17

Is 153 a perfect square?

No. 153 = 9 × 17: its largest perfect square factor is 9 = 3², and the factor 17 stays under the radical, so √153 = 3√17.

What is √153 as a decimal?

√153 ≈ 12.369. The decimal never ends and never repeats, so it is always rounded; the exact value is 3√17.

What is the largest perfect square that divides 153?

9 = 3². Dividing gives 153 ÷ 9 = 17, and 17 has no square factor left, so √153 = √9 × √17 = 3√17.

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