Radical Expression | MCQs

Explanation

A surd is an irrational number or expression containing a square root, cube root, etc., that can't be simplified to a rational number.

Example: √2, ³√5 are surds because they involve radical signs.

Explanation

To expand the expression:

(√3 - √2)²

= (√3)² - 2(√3)(√2) + (√2)²

= 3 - 2√6 + 2

= 5 - 2√6

Explanation

The expression √8-√2 simplifies to √2.

Explanation

Let's simplify the expression:

5√3 + √12

First, simplify √12:

√12 = √(4 × 3) = √4 × √3 = 2√3

Now add:

5√3 + 2√3 = 7√3

Explanation

The fourth root of 256 is:

⁴√256 = ⁴√(4^4) = 4

Explanation

Calculate the cube root of 32768.

³√32768 = ³√32³ = 32

Explanation

In the expression x√a, 'a' is called the radicand.

The radical symbol (✓) indicates a root, and the number or expression inside it (in this case, 'a') is the radicand.

Explanation

To simplify the expression:

2√3 + 4√12

First, simplify √12:

√12 = √(4 × 3) = √4 × √3 = 2√3

Now, substitute:

2√3 + 4(2√3) = 2√3 + 8√3 = 10√3

Explanation

Explanation

Let's simplify the expression:

∜256a⁴b⁴ = ∜(4⁴ × a⁴ × b⁴)

= ∜(4a × 4a × 4a × 4a × b × b × b × b)

= 4ab