What is the square root of 1?

The square root of 1 is 1. 1 = 1 squared, so sqrt(1) = 1 exactly. Verify: 1 x 1 = 1.

Is 1 a perfect square?

Yes. 1 = 1 squared, so sqrt(1) = 1 exactly.

How do you simplify sqrt(1)?

sqrt(1) = 1 (already fully simplified — it is an integer).

What is sqrt(1) squared?

(sqrt(1)) squared = 1. This follows from the definition: sqrt(n) is the number that when squared gives n. So (sqrt(1)) squared = 1 always.

What is the difference between square root and squaring?

Squaring 1: 1 squared = 1 (multiply 1 by itself). Square root of 1: sqrt(1) = 1 approximately 1.0000. They are inverse operations: sqrt(1) squared = 1 and sqrt(1 squared) = 1 (for non-negative numbers).

Square Root of 1 — sqrt(1) = 1

The square root of 1 is 1. 1 is a perfect square (1 squared = 1), so its square root is the exact integer 1. This page shows the exact value, simplified radical, decimal to 20 places, prime factorisation, and a visual number line....

√1 = ?

SQUARE ROOT OF 1

Exact — 1 is a perfect square (1² = 1)

Exact form

Decimal (4dp)

1.0000

Decimal (10dp)

1.0000000000

Is perfect sq?

Yes ✓

√1 ²

1 ✓

Between

1 (exact)

STEP-BY-STEP

Find a number that multiplied by itself equals 1

1 × 1 = 1 ✓

√1 = 1 (exact)

FUN FACT

sqrt(1)=1, the only square root equal to the original number (besides 0). 1 is both a perfect square (1 squared=1) and its own square root.

NUMBER LINE (√1 ≈ 1.0000)

√1

SQUARE WITH AREA = 1

Area = 1

√1

≈ 1.000

√1 ≈ 1.000

NEARBY PERFECT SQUARES

√1= 11² = 1you are here

√4= 22² = 4

√9= 33² = 9

√16= 44² = 16

SQUARE ROOT LAWS

√1 × √1= 1

(√1)²= 1

√(1 × 4)= 2√1 ≈ 2.0000

√(1/4)= √1/2 ≈ 0.5000

√1 × √2≈ 1.4142

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HOW TO CALCULATE

1
1 is a perfect square: 1 x 1 = 1. Perfect squares always have exact integer square roots.
2
Verify: 1 squared = 1. The square root of 1 is exactly 1.
3
Memorise the perfect squares: 1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256. These have exact integer square roots.
4
Check: sqrt(1) x sqrt(1) = 1 and (sqrt(1)) squared = 1. Both confirm the answer is 1.

WORKED EXAMPLE

sqrt(1): perfect square, 1 squared = 1. sqrt(1) = 1 (exact).

FREQUENTLY ASKED QUESTIONS

OTHER SQUARE ROOTS

√2 √3 √4 √5 √6 √7 √8 √9 √10 √11 √12 √13 √14 √15 √16 √17 √18 √19 √20 √21 √22 √23 √24 √25 √26 √27 √28 √29 √30

Bold bordered = perfect squares (exact integer result)

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Last updated: April 28, 2026 · Verified by EagleCalculator team · Eagle-eyed accuracy for every calculation.