Question
Rewrite expression to remove perfect square factors other than 1 in radicand. √98x8
The correct answer is: The given expression can be written as 7√2 × x4 after removing all perfect square factors other than 1
Hint:-
A radical expression refers to an expression containing a radical (√) symbol, commonly called as a root symbol.
A perfect square refers to a number that can be expressed as the product of an integer by itself.
We will simplify the given expressions, removing all the perfect square factors from under the radical sign.
Step-by-step solution:-
Given expression = √98x8
∴ Given expression = √(7 × 7 × 2 × x4+4 ) ….......................... (Factorizing the term inside the radical)
∴ Given expression = √(7 × 7 × 2 × x4 × x4 ............................... (Product property- an ⋅ am = an + m)
∴ Given expression = √(7 × 7) × √2 × √(x4 × x4) …..................... [Product property- √m × √n = √(m n)]
∴ Given expression = √(7)2 × √2 × √(x4)2
∴ Given expression = (7)2/2 × √2 × (x4)2/2 ............................ [Power rule- m√(b n) = b n/m]
∴ Given expression = (7)1 × √2 × (x4)1
∴ Given expression = 7 × √2 × x4
∴ Given expression = 7√2 × x4
"Final Answer:-
∴ The given expression can be written as 7√2 × x4 after removing all perfect square factors other than 1.
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A road sign shows a Vehicle's speed as the vehicle passes.
a. The sign blinks for vehicles travelling within 
of the speed limit. Write and solve an absolute value inequality to find the minimum and maximum speeds of an oncoming vehicle that will cause the sign to blink.
b. Another sign blinks when it detects a vehicle travelling within 
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|x|, which is pronounced "Mod x" or "Modulus of x," stands in for the absolute value of the variable x. The measure is the meaning of the Latin term "modulus." Common names for absolute value include numerical value and magnitude. The absolute value does not include the sign of the numeric value; it solely represents the numeric value. Any vector quantity's modulus is its absolute value and is always assumed to be positive.
Furthermore, absolute values express all quantities, including time, price, volume, and distance. Take the absolute value as an example: |+5| = |-5| = 5. The absolute value has no assigned sign. The formula to calculate a number's absolute value is |x| = x if it is greater than zero, |x| = -x if it is less than zero, and |x| = 0 if it is equal to zero.
A road sign shows a Vehicle's speed as the vehicle passes.
a. The sign blinks for vehicles travelling within of the speed limit. Write and solve an absolute value inequality to find the minimum and maximum speeds of an oncoming vehicle that will cause the sign to blink.
b. Another sign blinks when it detects a vehicle travelling within of a speed limit. Write and solve an absolute value inequality to represent the speeds of the vehicles that cause the sign to blink.
|x|, which is pronounced "Mod x" or "Modulus of x," stands in for the absolute value of the variable x. The measure is the meaning of the Latin term "modulus." Common names for absolute value include numerical value and magnitude. The absolute value does not include the sign of the numeric value; it solely represents the numeric value. Any vector quantity's modulus is its absolute value and is always assumed to be positive.
Furthermore, absolute values express all quantities, including time, price, volume, and distance. Take the absolute value as an example: |+5| = |-5| = 5. The absolute value has no assigned sign. The formula to calculate a number's absolute value is |x| = x if it is greater than zero, |x| = -x if it is less than zero, and |x| = 0 if it is equal to zero.
