Find the square of the following number using the column method and verify the result by finding the square using the prime factorization method of $90$.

A Pythagorean triplet whose one number is $6$. Then the other two numbers are $k$ and $k+2$. Then find the value of $k$.

Evaluate $69\times 71$.

Find the square of the following number using the shortcut methods.

$85$

Find the value of the following, using the column method: $(52{)}^2$

Evaluate $88\times 92$.

Write a Pythagorean triplet whose smallest member is $20$.

Using the formula $(a-b{)}^2=(a^2-2ab+b^2)$, evaluate ${196}^2$.

Find the value of the following, using the column method: $(96{)}^2$

Find the value of the following, using the column method: ${23}^2$

Using the formula $(a+b{)}^2=(a^2+2ab+b^2)$, evaluate ${310}^2$.

Between which two numbers does the square root of $2025$lie?