Simplify √98

asked by guest
on Jan 28, 2025 at 3:28 pm



You asked:

Simplify the expression: 98\sqrt{98}

MathBot Answer:

98=72\sqrt{98} = 7 \sqrt{2}


Given a positive integer nn, n\sqrt{n} simplifies to n=pq\sqrt{n} = p \sqrt{q} if nn can be written as the product n=p2qn = p^2 q, where pp and qq are positive integers. This simplification can be repeated until the integer under the square root sign is not divisible by the square of any integer. The number of tests to determine if n=p2qn = p^2 q for some integers pp and qq can be reduced by restricting pp to be prime. The first few squared prime numbers are: 22=42^2 = 4, 32=93^2 = 9, 52=255^2 = 25, 72=497^2 = 49, 112=12111^2 = 121, 132=16913^2 = 169, 172=28917^2 = 289, 192=36119^2 = 361


98=722=72 \begin{aligned} \sqrt{98} &= \sqrt{{7}^2 \cdot 2} \\ &= 7 \sqrt{2} \end{aligned}