Add or subtract, as indicated. See Example 6. -5√32 + 2√98

Guida verificata passo dopo passo

First, simplify each square root term by factoring the number inside the root into a product of a perfect square and another factor. For example, express 32 as 16 \(\times\) 2 and 98 as 49 \(\times\) 2.

Rewrite each term using the property \( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \). So, \( \sqrt{32} = \sqrt{16} \times \sqrt{2} \) and \( \sqrt{98} = \sqrt{49} \times \sqrt{2} \).

Calculate the square roots of the perfect squares: \( \sqrt{16} = 4 \) and \( \sqrt{49} = 7 \). Substitute these back into the expression.

Rewrite the original expression with the simplified roots: \( -5 \times 4 \times \sqrt{2} + 2 \times 7 \times \sqrt{2} \).

Factor out the common radical \( \sqrt{2} \) and combine the coefficients: \( (-5 \times 4 + 2 \times 7) \times \sqrt{2} \). This will give you the simplified expression.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Durata del video:

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Simplifying Radicals

Simplifying radicals involves expressing the number under the square root as a product of perfect squares and other factors. This allows you to extract the square root of the perfect square, making the radical simpler. For example, √32 can be written as √(16×2) = 4√2.

Video consigliato:

Percorso guidato

6:36

Simplifying Trig Expressions

Like Radicals

Like radicals have the same radicand (the number inside the root) and the same index. Only like radicals can be added or subtracted directly by combining their coefficients. For instance, 4√2 and 2√2 are like radicals and can be combined as (4+2)√2 = 6√2.

Video consigliato:

Percorso guidato

2:58

Rationalizing Denominators

Adding and Subtracting Radicals

To add or subtract radicals, first simplify each radical to identify like terms. Then, combine the coefficients of like radicals by addition or subtraction. If radicals are not like terms, they remain separate in the expression.

Video consigliato:

Percorso guidato