When square root of 189 is written as a simplified mixed radical the coefficient is Answer __ and the radicand is Answer __.
The square root of 189 can be simplified as $\sqrt{189} = \sqrt{9 \cdot 21} = \sqrt{9} \cdot \sqrt{21} = 3 \cdot \sqrt{21}$.
Therefore, the coefficient is $\boxed{3}$ and the radicand is $\boxed{21}$.
The velocity of a falling object can be found using the formula v space equals space square root of 64 h end root, where v is the velocity of the object in feet per second, and h is the distance the object has already fallen in feet. Determine the exact velocity of an object after it has fallen 7 feet in simplified form.
To find the exact velocity of an object after it has fallen 7 feet using the formula $v = \sqrt{64h}$, we substitute $h = 7$ into the formula:
$v = \sqrt{64 \cdot 7} = \sqrt{448} = \sqrt{64 \cdot 7} = \sqrt{64} \cdot \sqrt{7} = 8 \cdot \sqrt{7} = \boxed{8\sqrt{7}}$ feet per second.
To simplify the square root of 189, we can rewrite it as the product of the square root of a perfect square and a non-perfect square.
First, we can factorize 189. The prime factorization of 189 is 3 × 3 × 3 × 7.
Now, we can group the prime factors into perfect squares and non-perfect squares. The perfect squares are 3 × 3 = 9, and the non-perfect square is 7.
Therefore, we can rewrite the square root of 189 as the square root of 9 times the square root of 7.
√189 = √9 × √7
The simplified mixed radical form of the square root of 189 is 3√7.
The coefficient is 3, and the radicand is 7.
To simplify the square root of 189, we need to factorize the radicand (189) into its prime factors.
First, we know that 9 is a perfect square factor of 189, since 9 x 21 = 189. Thus, we rewrite 189 as:
√(9 x 21)
Now, we can simplify the square root further by taking the square root of the perfect square factor separately and leaving the remaining factor inside the square root. Thus, we have:
√9 x √21
The square root of 9 is 3, so we can substitute that value:
3√21
Therefore, the coefficient is 3, and the radicand is 21.