What is the square root of 17?

The square root of 17 is sqrt17. In decimal: sqrt(17) approximately 4.1231056256 This is irrational — the decimal never terminates or repeats. sqrt(17)=4.12310... is irrational. 17 is prime.

Is 17 a perfect square?

No. 17 is not a perfect square. 4 squared = 16 and 5 squared = 25. Since 17 falls between these, sqrt(17) is not an integer. Nearest perfect squares: 16 (= 4 squared) and 25 (= 5 squared).

How do you simplify sqrt(17)?

sqrt(17) simplifies to sqrt17. Method: prime factorisation of 17 = 17. Since no factor repeats, sqrt(17) cannot be simplified further.

What is sqrt(17) squared?

(sqrt(17)) squared = 17. This follows from the definition: sqrt(n) is the number that when squared gives n. So (sqrt(17)) squared = 17 always.

What is the difference between square root and squaring?

Squaring 17: 17 squared = 289 (multiply 17 by itself). Square root of 17: sqrt(17) = sqrt17 approximately 4.1231. They are inverse operations: sqrt(17) squared = 17 and sqrt(17 squared) = 17 (for non-negative numbers).

Square Root of 17 — sqrt(17) = sqrt17

The square root of 17 is sqrt17. In decimal form, sqrt(17) approximately 4.123106 (irrational). This page shows the exact value, simplified radical, decimal to 20 places, prime factorisation, and a visual number line....

√17 = ?

SQUARE ROOT OF 17

√17

≈ 4.1231056256

Irrational — cannot be expressed as a fraction

Exact form

√17

Decimal (4dp)

4.1231

Decimal (10dp)

4.1231056256

Is perfect sq?

√17 ²

17 ✓

Between

4 and 5

DECIMAL PRECISION

√17 ≈ 4.1231056256

STEP-BY-STEP

Prime factorisation: 17 = 17

Simplified radical form: √17

4² = 16 < 17 < 25 = 5² → lies between 4 and 5

√17 ≈ 4.1231056256...

FUN FACT

sqrt(17)=4.12310... is irrational. 17 is prime.

NUMBER LINE (√17 ≈ 4.1231)

√17

SQUARE WITH AREA = 17

Area = 17

√17

≈ 4.123

√17 ≈ 4.123

NEARBY PERFECT SQUARES

√4= 22² = 4

√9= 33² = 9

√16= 44² = 16

√25= 55² = 25

√36= 66² = 36

√49= 77² = 49

SQUARE ROOT LAWS

√17 × √17= 17

(√17)²= 17

√(17 × 4)= 2√17 ≈ 8.2462

√(17/4)= √17/2 ≈ 2.0616

√17 × √18≈ 17.4929

Created with❤️byeaglecalculator.com

HOW TO CALCULATE

1
Find the prime factorisation of 17: 17 = 17. Check for repeated prime factors.
2
Simplify: pull out any pairs of identical prime factors. Result: sqrt17. Since no factor repeats, it cannot be simplified further.
3
Locate sqrt(17) between integers: 4 squared = 16 and 5 squared = 25. Since 16 < 17 < 25, sqrt(17) lies between 4 and 5.
4
Calculate decimal: sqrt(17) approximately 4.1231056256. Verify by squaring: (4.123106) squared approximately 17.0 = 17.

WORKED EXAMPLE

sqrt(17): not a perfect square. Factorisation: 17 = 17. Simplified: sqrt17. Decimal: sqrt(17) approximately 4.1231056256.

FREQUENTLY ASKED QUESTIONS

OTHER SQUARE ROOTS

√1 √2 √3 √4 √5 √6 √7 √8 √9 √10 √11 √12 √13 √14 √15 √16 √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.