Does the square root of ((a^2)-(10a)+(25))simplify to a+5 times the square root of -10a ? Thank You.
a^2 + 10a + 25
= (a+5)^2
so √(a+5)^2 = a+5 , just like √(7^2) = 7
To determine if the square root of ((a^2) - 10a + 25) simplifies to a + 5 times the square root of -10a, we need to simplify the expression and compare the results.
First, simplify the expression ((a^2) - 10a + 25):
(a^2) - 10a + 25 = (a - 5)^2
Now, take the square root of both sides:
√((a^2) - 10a + 25) = √((a - 5)^2)
The square root of a perfect square is equal to the positive and negative value of the square root of its perfect square. Thus:
√((a^2) - 10a + 25) = ± (a - 5)
So, the square root of ((a^2) - 10a + 25) simplifies to ± (a - 5), not a + 5 times the square root of -10a.
Please note that √(ab) = √a * √b does not apply if both a and b are negative. In this case, we need to express the square root of -10a as ± √(10a), not √(-10) * √a.
To determine if the square root of ((a^2)-(10a)+(25)) simplifies to a+5 times the square root of -10a, we will simplify the expression and see if it matches.
First, let's simplify the expression within the square root:
((a^2)-(10a)+(25))
To simplify, we can factor this expression:
(a-5)(a-5)
Now, let's rewrite the expression within the square root using the factored form:
√((a-5)(a-5))
Next, we can simplify the square root by separating the factors and taking the square root individually:
√(a-5) * √(a-5)
The square root of (a-5) can be written as (a-5)^(1/2). Now we have:
(a-5)^(1/2) * (a-5)^(1/2)
Using the property of exponents that when you multiply two terms with the same base, you add the exponents, we can simplify further:
(a-5)^(1/2 + 1/2)
The exponents 1/2 + 1/2 add up to 1, so we have:
(a-5)^1
And since any number raised to the power of 1 is equal to itself, we can rewrite this as:
(a-5)
So the simplified expression is just (a-5), which means the original expression does not simplify to a+5 times the square root of -10a.
Therefore, the statement "The square root of ((a^2)-(10a)+(25)) simplifies to a+5 times the square root of -10a" is incorrect.