Question
Find the square root of the following by prime factorization.$27225$
✓
Answer
Resolving $27225$ into prime factors, $27225 = 3 \times 3 \times 5 \times 5 \times 11 \times 11$
$\begin{array}{c|c}3&27225 \\ \hline 3 & 9075 \\\hline 5&3025\\\hline5&605 \\\hline11&121\\\hline11&11\\\hline&1\end{array}$
Grouping the factors into pairs of equal factors, $27225 = (3 \times 3) \times (5 \times 5) \times (11 \times 11)$
Taking one factor for each pair, we get the square root of $27225 3 \times 5 \times 11 = 165$
$\begin{array}{c|c}3&27225 \\ \hline 3 & 9075 \\\hline 5&3025\\\hline5&605 \\\hline11&121\\\hline11&11\\\hline&1\end{array}$
Grouping the factors into pairs of equal factors, $27225 = (3 \times 3) \times (5 \times 5) \times (11 \times 11)$
Taking one factor for each pair, we get the square root of $27225 3 \times 5 \times 11 = 165$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The figure shows the dimensions of a wall having a window and a door of a room. Write an algebraic expression for the area of the wall to be painted.
Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table.
.
Calculate the angle between a pair of consecutive spokes on a wheel with $15$ spokes?
→.
| Numbers of spokes | $4$ | $6$ | $8$ | $10$ | $12$ |
| Angle between a pair of consecutive spokes | $90^\circ $ | $60^\circ $ | – | – | – |
Write five numbers for which you cannot decide whether they are squares.
Find the cube root of each of the following natural numbers: $17576$
→Solve the following equation and verify your answer: $\frac{2\text{y}+5}{\text{y}+4}=1$
→Take away: $\frac{\text{y}^3}{3}+\frac{7\text{y}^2}{3}+\frac{1}{2}\text{y}+\frac{1}{2}$ from $\frac{1}{3}−\frac{5}{3}\text{y}^2$
→If you put $21$ consonants and $5$ vowels in a bag. What would carry greater probability$?$ Getting a consonant or a vowel$?$ Find each probability.
→If we fix time period and the rate of interest, simple interest changes proportionally with principal. Would there be a similar relationship for compound interest? Why?
Plot the given points on a graph sheet and check if the points lie on a straight line. If not, name the shape they form when joined in the given order. $(4, 2), (2, 4), (3, 3), (5, 4)$
→In the year $2001,$ the number of malaria patients admitted in the hospitals of a state was $4375.$ Every year this number decreases by $8 \%$. Find the number of patients in $2003.$
→