Square Root of 98 Simplified

Simplify Square Root Calculator
Simplify the square root of

What is the square root of 98 simplified?

Answer

√98 = 7√2

98 = 49 × 2, and 49 = 7² is the largest perfect square that divides 98, so √98 = √49 × √2 = 7√2. Check: 7√2 ≈ 9.899, the same as √98 ≈ 9.899.

Simplifying √98 Step by Step

1. Prime factorization. — All Prime Factors of 98:

98 = 2 × 7 × 7 = 2 × 72

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 98Comes out of the rootStays under the root
21—2
727—

3. Take the pairs out of the root.

√98 = √((7 × 7) × 2)

= 7 × √2

= 7√2

4. Check by squaring back.

7² × 2 = 49 × 2 = 98

Related Calculations

See Also

Simplify Square Root Calculator

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 98 simplified? (The answer is: 7√2). Enter a whole number (e.g. '98') and hit the 'Simplify' button.
Recalculate with different values ↑

Simplified Square Roots Table

NumberSimplest radical formDecimal value
83√83≈ 9.11
842√21≈ 9.165
85√85≈ 9.22
86√86≈ 9.274
87√87≈ 9.327
882√22≈ 9.381
89√89≈ 9.434
903√10≈ 9.487
91√91≈ 9.539
922√23≈ 9.592
93√93≈ 9.644
94√94≈ 9.695
95√95≈ 9.747
964√6≈ 9.798
97√97≈ 9.849
987√2≈ 9.899
993√11≈ 9.95
1001010
101√101≈ 10.05
102√102≈ 10.1
103√103≈ 10.149
1042√26≈ 10.198
105√105≈ 10.247
106√106≈ 10.296
107√107≈ 10.344
1086√3≈ 10.392
109√109≈ 10.44
110√110≈ 10.488
111√111≈ 10.536
1124√7≈ 10.583

FAQ

What is the square root of 98 simplified?

√98 = 7√2

Is 98 a perfect square?

No. 98 = 49 × 2: its largest perfect square factor is 49 = 7², and the factor 2 stays under the radical, so √98 = 7√2.

What is √98 as a decimal?

√98 ≈ 9.899. The decimal never ends and never repeats, so it is always rounded; the exact value is 7√2.

What is the largest perfect square that divides 98?

49 = 7². Dividing gives 98 ÷ 49 = 2, and 2 has no square factor left, so √98 = √49 × √2 = 7√2.

See Also