Pregunta 1: Simplifique cada uno de los siguientes:
![\\(i)\sqrt[3]{4} \times \sqrt[3]{16}\\ (ii)\frac{\sqrt[4]{1250}}{\sqrt[4]{2}}](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-a2694a3e8688e5f9f5c2c25c7d63e765_l3.png "Rendered by QuickLaTeX.com")
Solución:
(i)
Usando la fórmula:
Aquí,
(ii)
Usando la fórmula:
Aquí,
![\sqrt[n]{a}\times\sqrt[n]{b}= \sqrt[n]{a \times b}\\](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-101b0c8fef0fc1f9c5b0ad27ea8f7cbb_l3.png "Rendered by QuickLaTeX.com")
![\\=\sqrt[3]{4\times 16}\\ =\sqrt[3]{64}\\ =\sqrt[3]{4^{3}}\\ =(4^{3})^{\frac{1}{3}}\\ = 4](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-29456be285e1c45d106120d247d0a3b1_l3.png "Rendered by QuickLaTeX.com")
![\\ \frac{\sqrt[n]{a}}{\sqrt[n]{b}} = \sqrt[n]{\frac{a}{b}}](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-469e695e323580f1035f9f532f5ddbbc_l3.png "Rendered by QuickLaTeX.com")
![\\= \sqrt[4]{\frac{1250}{2}}\\ = \sqrt[4]{\frac{2\times 625}{2}}\\ = \sqrt[4]{625}\\ = \sqrt[4]{5^{4}}\\ =5^{(4\times \frac{1}{4})}\\ = 5](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-268e24bd9b3341822481a166dfbac30e_l3.png "Rendered by QuickLaTeX.com")
Pregunta 2: Simplifica las siguientes expresiones:
(i) (4 + √7) (3 + √2)
(ii) (3 + √3)(5- √2)
(iii) (√5 -2)( √3 – √5)
Solución:
(i) (4 + √7) (3 + √2)
= 12 + 4√2 + 3√7 + √14
(ii) (3 + √3)(5- √2)
= 15 – 3√2 + 5√3 – √6
(iii) (√5 – 2)(√3 – √5)
= √15 – √25 – 2√3 + 2√5
= √15 – 5 – 2√3 + 2√5
Pregunta 3: Simplifica las siguientes expresiones:
(yo) (11 + √11) (11 – √11)
(ii) (5 + √7) (5 –√7)
(iii) (√8 – √2) (√8 + √2)
(iv) (3 + √3) (3 – √3)
(v) (√5 – √2) (√5 + √2)
Solución:
Usando Identidad: (a – b)(a + b) = a 2 – b 2
(yo) (11 + √11) (11 – √11)
= 11 2 – (√11) 2
= 121 – 11
= 110
(ii) (5 + √7) (5 –√7)
= (5 2 – (√7) 2 )
= 25 – 7 = 18
(iii) (√8 – √2) (√8 + √2)
= (√8) 2 – (√2) 2
= 8 – 2
= 6
(iv) (3 + √3) (3 – √3)
= (3) 2 – (√3) 2
= 9 – 3
= 6
(v) (√5 – √2) (√5 + √2)
= (√5) 2 – (√2) 2
= 5 – 2
= 3
Pregunta 4: Simplifica las siguientes expresiones:
(yo) (√3 + √7) 2
(ii) (√5 – √3) 2
(iii) (2√5 + 3√2 ) 2
Solución:
Usando identidades: (a – b) 2 = a 2 + b 2 – 2ab y (a + b) 2 = a 2 + b 2 + 2ab
(yo) (√3 + √7) 2
= (√3) 2 + (√7) 2 + 2(√3)(√7)
= 3 + 7 + 2√21
= 10 + 2√21
(ii) (√5 – √3) 2
= (√5) 2 + (√3) 2 – 2(√5)(√3)
= 5 + 3 – 2√15
= 8 – 2√15
(iii) (2√5 + 3√2) 2
= (2√5) 2 + (3√2) 2 + 2(2√5)( 3√2)
= 20 + 18 + 12√10
= 38 + 12√10
Publicación traducida automáticamente
Artículo escrito por nidhi_biet y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA