simplify √50y^7
√50y^7 can be simplified as 5y^3√2y.
To simplify the expression √50y^7, we can break it down further.
First, we can separate the square root of 50 by factoring out the perfect square that is the largest factor of 50.
√50 = √(25 * 2) = √25 * √2 = 5√2
Next, we can simplify the variable term y^7. Since y^7 can be written as y^6 * y, we can rewrite it as:
y^7 = y^6 * y = (y^3)^2 * y = y^3y^3y = y^6y
Combining the simplified terms:
√50y^7 = 5√2y^6y
So, the simplified form of √50y^7 is 5√2y^6y.
To simplify the expression √50y^7, we can break down the square root of 50 and y^7 into their prime factors.
First, let's start with 50. The prime factorization of 50 is 2 * 5^2.
Next, for y^7, we can write it as y^6 * y.
Now, let's put it all together.
√50y^7 = √(2 * 5^2 * y^6 * y)
Taking the square root of each prime factor separately:
√50y^7 = √2 * √(5^2) * √(y^6) * √y
Simplifying further:
√50y^7 = √2 * 5 * y^3 * √y
Combining like terms:
√50y^7 = 5y^3√2y
Therefore, √50y^7 simplifies to 5y^3√2y.