Is 50 a Perfect Square?

No, 50 is not a perfect square.

Quick math

  • √50 ≈ 7.0711
  • 72 = 49 < 50 < 64 = 82
  • 50 = 2 × 52
Perfect square
No
Square root
≈ 7.0711
Simplest radical form
5√2
Prime factorization
2 × 5²
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Is 50 a Perfect Square?

No, 50 is not a perfect square. It lies between 7² = 49 and 8² = 64.

Handwritten notebook page checking whether 50 is a perfect square
50 lies between two consecutive perfect squares, so it is not a perfect square.

Step 1: The Square Root of 50

√50 ≈ 7.0711. The root is not a whole number, so the number is not a perfect square.

Step 2: Prime Factorization

50 = 2 × 5². At least one exponent is odd, so the number cannot be a perfect square.

Step 3: Simplest Radical Form

√50 = 5√2. Pull the square factors out of the root: 5² comes out as 5.

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Is 50 a Perfect Square?: FAQs

Is 50 a perfect square?

No. No whole number multiplied by itself gives 50. It sits between 7² = 49 and 8² = 64.

What is the square root of 50?

The square root of 50 is about 7.0711, which simplifies to 5√2.

How do you check if 50 is a perfect square using prime factors?

Write 50 as 2 × 5². The exponent of 2 is odd, so the primes cannot all be paired and 50 is not a perfect square.

What is the next perfect square after 50?

The next perfect square after 50 is 8² = 64.

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