Square Root of 20 Simplified: Value, Methods & Examples

Anyone who’s grappled with square roots in math class knows that some numbers are simpler than others. The square root of 20 is approximately 4.4721, as BYJU’s notes, and its exact simplified form is 2√5 — here you’ll find two straightforward methods to work out the value yourself.

Exact simplified form: 2√5 · Decimal approximation: 4.47213595 · Rounded to nearest tenth: 4.5

Five key properties of √20, one pattern: the number sits between the perfect squares 16 and 25, and its simplified radical form is a product of 2 and √5.

What is the square root of 20?

What is the value of √20?

The square root of 20 is the number that when multiplied by itself gives 20. Its exact value in simplified radical form is 2√5 (Testbook, test prep resource). In decimal form, it is approximately 4.472135955 (BYJU’S, educational platform).

What is the decimal representation of √20?

Rounded to four decimal places, √20 equals 4.4721 (Testbook). Because √20 lies between √16 (4) and √25 (5), its decimal starts with 4. The remaining digits come from the iterative long division process.

The implication: for pure math, the radical form preserves accuracy, while decimals are best for applied contexts.

Is 20 a perfect square?

What defines a perfect square?

A perfect square is an integer that is the square of an integer. For example, 16 = 4² and 25 = 5² are perfect squares. To qualify, every prime factor must appear in pairs (Cuemath, math learning platform).

Why 20 is not a perfect square

The prime factorization of 20 is 2 × 2 × 5 (Vedantu, online tutoring platform). The factor 5 has no pair, so 20 cannot be written as the square of an integer. As Cuemath confirms, “20 is not a perfect square because the prime factor 5 does not have a pair.”

The pattern: this property makes radical simplification the only way to represent the value exactly.

How to simplify the square root of 20?

Step-by-step simplification using prime factorization

• Factor 20: 20 = 2 × 2 × 5 (Vedantu).
• Group identical factors into pairs: (2 × 2) × 5.
• Take one factor from each pair out of the square root: √(2×2) = 2.
• Leave the unpaired factor inside: √5.
• Multiply: 2 × √5 = 2√5 (BYJU’S).

WorkyBooks (educational resource) notes that prime factorization is effective for simplifying radicals into their simplest form.

What is the simplified radical form of √20?

The simplest radical form is 2√5. This is obtained by factoring out the largest perfect square factor of 20, which is 4: √20 = √(4 × 5) = √4 × √5 = 2√5. Both Testbook and BYJU’S confirm this result.

The consequence: you never need to approximate when doing algebra — the radical form is exact.

Is root 20 equal to 2 root 5?

Verification of the equality

Yes. Squaring 2√5 gives (2√5)² = 4 × 5 = 20, which by definition is the square of √20. Because squaring both sides yields the same result, √20 = 2√5 (BYJU’S).

Why 2√5 is the simplest form

The expression 2√5 is already in simplest radical form because the number under the radical (5) is a prime with no square factors. Testbook emphasizes that this radical cannot be simplified further.

What is the square root of 20 using the division method?

Steps for long division method

1. Write 20 as 20.0000 and pair the digits from the decimal point: 20 | 00 00 00.
2. Find the largest integer whose square is ≤ 20: 4 (since 4² = 16). Write 4 as the first digit of the quotient.
3. Subtract 16 from 20, leaving remainder 4. Bring down two zeros to make 400.
4. Double the current quotient (4 → 8). Find a digit X such that (8X) × X ≤ 400. 87 × 7 = 609 (too high), 86 × 6 = 516 (too high), 84 × 4 = 336 (≤400). So X = 4. New divisor is 84.
5. Subtract 336 from 400 → remainder 64. Bring down two zeros → 6400.
6. Double the quotient (now 44 → 88). Find digit Y such that (88Y) × Y ≤ 6400. 882 × 2 = 1764 (too low), 883 × 3 = 2649 (still low), 884 × 4 = 3536, 885 × 5 = 4425, 886 × 6 = 5316, 887 × 7 = 6209, 888 × 8 = 7104 (>6400). So Y = 7. Subtract 6209 from 6400 → remainder 191.
7. Continue bringing down pairs of zeros to reach desired precision. The quotient becomes 4.4721…

WorkyBooks describes this iterative process as the most precise method for obtaining decimal values of square roots.

Estimation of √20 to decimal places

After enough iterations, the long division method yields the decimal 4.472135955 (BYJU’S). Rounded to the nearest tenth it is 4.5, to the nearest hundredth it is 4.47, and to the thousandth it is 4.472.

The takeaway: long division gives you decimal precision, but the radical form is the only exact representation.

“By using prime factorization, you can simplify √20 to 2√5 in just a few steps.”

— Mathway (algebra solver)

“20 is not a perfect square because the prime factor 5 does not have a pair.”

— Cuemath (math learning platform)

For learners and teachers alike, the choice between prime factorization and long division depends on the goal: simplification vs. decimal accuracy. Prime factorization gives the clean radical form 2√5; long division delivers the decimal to as many places as needed. The implication: master both methods, and you’ll never be stuck with an ugly square root again.

For a similar step-by-step breakdown, see our guide on simplifying the square root of 8, which follows the same prime factorization approach.

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